160505(6)

Ruby


Somos' sequence(2)

さらに調べてみた。

def b(k, n)
  b = Array.new(2 * k + 3, 1)
  (2 * k + 3..n).each{|i|
    j = (b[i - 1] * b[i - 2 * k - 2] + b[i - k - 1] * b[i - k - 2]) / b[i - 2 * k - 3].to_r
    j = j.to_i if j.denominator == 1
    b[i] = j
  }
  b[0..n]
end

(20..50).each{|i| p [i, b(i, 200)]}

出力結果
[20, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 30, 42, 62, 92, 134, 190, 262, 352, 462, 594, 750, 932, 1142, 1382, 1654, 1960, 2302, 2682, 3102, 3564, 7656, 11844, 16212, 20916, 26240, 32668, 40972, 52316, 68376, 91476, 124740, 172260, 239280, 332396, 459772, 631372, 859208, 1157604, 1543476, 2036628, 2660064, 4142160, 8955936, 18938808, 36030864, 62317344, 100084048, 151898824, 220742016, 310222704, 424936512, 571045464, 757191600, 995894592, 1305630192, 1713841768, 2261202208, 3007518864, 4039760736, 5482785528, 7513455312, 10378954080, 25387116480, 44119896480, 74711796192, 138480973632, 281080918656, 587626657728, 1202365881376, 2353642148000, 4385117757504, 7794518336352, 13281585169248, 21807573270912, 34669680435456, 53595507963008, 80865466021792, 119475596171744, 173360548664512, 247707797408544, 349411527614688, 487740635236800, 675333498702720, 1150660706342400, 2758300160964480, 6200936883504000, 12343505240698368, 22429071407648256, 38672426413735424, 65753119195499648, 114183998588604032, 207225917397137408, 394032215329627776, 773136360594449280, 1532367481740336384, 3013950609590981632, 5817125721405880576, 10955367642996291712, 20091557989415553408, 35882723923410567680, 62476874583535398272, 106218979721245531008, 176642648689004332032, 287850721027447226880, 778958981983447034880, 1478760192728891297280, 2891776398381595456512, 6384497929441683812352, 14958111929034292572160, 34357266151315458043904, 74627038587409203121152, 152327424044635557684736, 293857575834238536006656, 540950569996059070650880, 960844708741552408181760, 1666850765451890760135680, 2861742684627974192779264, 4929641124738252831284224, 8626963253987810923709440, 15467937597484094790445568, 28478367852148480916122624, 53623239475980713978234368, 102430396462403990569149440, 196680026633001696264640512, 376575809007924851542429696, 973644713704193325865635840, 3335038629290185712865890304, 9047821633650385748361388032, 20987856613402873777700667392, 45873368891018160422435323904, 102008427984889775761198022656, 239740668244575582979232456704, 589208438330951658423952076800, 1461341595990930947339488268288, 3545782780436044243564881719296, 8276336198724564493539209543680]]
[21, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 31, 43, 63, 93, 135, 191, 263, 353, 463, 595, 751, 933, 1143, 1383, 1655, 1961, 2303, 2683, 3103, 3565, 4071, 8717, 13463, 18395, 23671, 29577, 36599, 45511, 57479, 74181, 97943, 131891, 180119, 247873, 341751, 469919, 642343, 871037, 1170327, 1557131, 2051255, 2675705, 3457015, 5300534, 11266941, 23617108, 44728043, 77140082, 123617201, 187233648, 271509823, 380634286, 519827717, 695929356, 918317683, 1200315626, 1561277177, 2029607720, 2647035399, 3474526246, 4600322317, 6150680516, 8304000891, 11309157730, 15508985537, 37709617409, 65091818633, 108702114401, 197305505417, 392295629185, 807839495361, 1636954090881, 3184422641073, 5907715923329, 10467419859289, 17789141041057, 29139566224441, 46220458492929, 71286155823697, 107293026999233, 158093987097121, 228698539887617, 325630273709993, 457431219287265, 635388629604201, 874598130920577, 1195532549826913, 2002247268081345, 4719107435965913, 10519917366605857, 20831629425236121, 37657710386424769, 64454853148219297, 108322412614340097, 184920569112935153, 328532397644751425, 611134618616829321, 1176376152670921697, 2297151086552263273, 4469205517466106689, 8558205156709309841, 16024256977186619073, 29256470253923508481, 52061350531526778817, 90363444859706185145, 153195816343762314145, 254083233052319488185, 412954804799412373697, 658768831991706104833, 1756122109482775623586, 3281868401819491670347, 6243344605647194093636, 13348344611975743637309, 30515969147343030375142, 69027603915837954517063, 148515793669939573145192, 301149617361901001393497, 577768404233521300369706, 1057688296318846851551971, 1866199190889300997318156, 3208842323329369156155861, 5442105846903825660124526, 9220920713770329864227999, 15802217987191214608671280, 27653696863155871306012721, 49638139896378945788402354, 91247299039359412906639611, 170692559773060717438938580, 322191826290711206530128877, 608624773818443234914141174, 1143007796165579308198982519, 2881948089716015588746477561, 9670925579361578182965663303]]
[22, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 32, 44, 64, 94, 136, 192, 264, 354, 464, 596, 752, 934, 1144, 1384, 1656, 1962, 2304, 2684, 3104, 3566, 4072, 4624, 9872, 15224, 20768, 26664, 33200, 40864, 50432, 63072, 80464, 104936, 139616, 188600, 257136, 351824, 480832, 654128, 883728, 1183960, 1571744, 2066888, 2692400, 3474816, 4444544, 6716928, 14047424, 29195584, 55051712, 94689152, 151429888, 228936704, 331354880, 463540352, 631430208, 842636096, 1107372352, 1439869184, 1860467840, 2398650112, 3097319552, 4018727168, 5252520896, 6926496576, 9220739264, 12385968256, 16767037952, 22832700416, 55202876416, 94688424448, 156109560320, 277820310016, 541420425216, 1098294335488, 2203823398912, 4260367296512, 7870410829824, 13901655544320, 23566358788608, 38517986355712, 60969418157056, 93838804696064, 140932146563072, 207176413086720, 298924490949632, 424364837065216, 594086332705280, 821875146953216, 1125858986784768, 1530169670496256, 2067373691846656, 3407960631402496, 7905420656205824, 17482574821658624, 34450966301786112, 61988088128471040, 105413218071281664, 175351126580199424, 294808772305289216, 513608258905309184, 935667214792114176, 1767477002526789632, 3400025070451548160, 6541621277952761856, 12425971422111809536, 23128839421425565696, 42038320913975361536, 74538852803785170944, 128988583484847562752, 218094959413567393792, 360826215694676819968, 585039595989947531264, 931064584202652614656, 1456557282795395874816, 3830106743130038730752, 7057750621718428057600, 13095470346583270490112, 27163481972854196404224, 60623406166187053154304, 135046082557468941484032, 287811775953795746365440, 579846338324986026524672, 1106722682079721429139456, 2015885099458933023440896, 3536330018960054635724800, 6034949175448602726563840, 10130047105203411845120000, 16924509731471197662478336, 28480816569620955326840832, 48767092251481068754567168]]
[23, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 33, 45, 65, 95, 137, 193, 265, 355, 465, 597, 753, 935, 1145, 1385, 1657, 1963, 2305, 2685, 3105, 3567, 4073, 4625, 5225, 11125, 17133, 23339, 29905, 37121, 45477, 55751, 69113, 87245, 112477, 147939, 197729, 267097, 362645, 492543, 666761, 897317, 1198541, 1587355, 2083569, 2710193, 3493765, 4464695, 5657625, 8435360, 17369315, 35802614, 67224949, 115330364, 184088543, 277842898, 401458481, 560556696, 761892731, 1013956334, 1327907789, 1718999476, 2208679991, 2827633226, 3620069833, 4649663888, 6007614099, 7823407334, 10278973349, 13627044140, 18214670095, 24512998850, 33154592225, 79726113325, 135951813445, 221493390205, 386931262449, 739553694413, 1477968859493, 2936559934941, 5641097999521, 10377177009517, 18273572244773, 30903206564413, 50405238945777, 79633037643277, 122334742371973, 183376188670109, 269020817825249, 387288790380717, 548429240102277, 765557380702461, 1055534660890225, 1440208926482765, 1948187325925925, 2617393671359325, 3498772111198625, 5683778810524725, 12988450313416925, 28506184676476645, 55918529528510225, 100189898388705013, 169399012284051837, 279248538727454373, 463111051172028513, 792457223478462005, 1415370644286959101, 2624826207302885093, 4973794735936598417, 9461404578894297589, 17823799571971210845, 32975554167268440997, 59663261685373830817, 105413121300289743413, 181880211370634140317, 306740246915421853925, 506307163136788007825, 819114926697262651125, 1300774016348042164925, 2030508647779623785125, 3119909998602613398625, 8102182137481503865250, 14742093701897503069175, 26741294462536401665500, 53911616705286358093925, 117522184198473765948550, 257812515593160048657787, 544251203597994986986176, 1089539301443255959108745]]
[24, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 34, 46, 66, 96, 138, 194, 266, 356, 466, 598, 754, 936, 1146, 1386, 1658, 1964, 2306, 2686, 3106, 3568, 4074, 4626, 5226, 5876, 12480, 19196, 26116, 33404, 41352, 50452, 61484, 75620, 94544, 120588, 156884, 207532, 277784, 374244, 505084, 680276, 911840, 1214108, 1604004, 2101340, 2729128, 3513908, 4486092, 5680324, 7135856, 10505248, 21312304, 43579080, 81491264, 139461872, 222208640, 334858456, 483101904, 673434944, 913543696, 1212913000, 1583770656, 2042517776, 2611842272, 3323767928, 4223956528, 5377655904, 6877773296, 8855651848, 11495239168, 15051461424, 19873755200, 26435863064, 35373168272, 47529030016, 113704259968, 192833174144, 310731494944, 533427369056, 1000575164480, 1970174383520, 3875815505760, 7398021049536, 13551655723008, 23791877941312, 40141755430816, 65345572561568, 103053188165824, 158042837674592, 236492946314976, 346318487191040, 497595143914112, 703106403709952, 979066647921952, 1346099976013536, 1830593470944576, 2466599625243936, 3298541884717664, 4385087703360832, 5804705290598656, 9302895382084096, 20960198924051712, 45670591326199424, 89205804680370560, 159213909008972800, 267815233025212800, 437949792810940800, 717460584179189760, 1207650927875039232, 2116999190040963072, 3856174148620173952, 7197862874965902464, 13534682168223663616, 25281186739689695360, 46482444707443362176, 83712735421327757056, 147374784571276307968, 253544056055146271488, 426545888052622589568, 702508262221290874752, 1134203268470356850688, 1797580880145212782464, 2800516742335613448576, 4294452016113189998080, 6489813940394704331776]]
[25, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 35, 47, 67, 97, 139, 195, 267, 357, 467, 599, 755, 937, 1147, 1387, 1659, 1965, 2307, 2687, 3107, 3569, 4075, 4627, 5227, 5877, 6579, 13941, 21419, 29107, 37171, 45905, 55803, 67647, 82611, 102381, 129291, 166475, 218035, 289225, 386651, 518487, 694707, 927333, 1230699, 1621731, 2120243, 2749249, 3535291, 4508783, 5704371, 7161309, 8923851, 12981834, 25964361, 52679080, 98115631, 167515686, 266456877, 400964004, 577670643, 804068226, 1088898609, 1442770848, 1879114135, 2415617374, 3076352469, 3894833820, 4918331547, 6213831354, 7876120473, 10038577560, 12887355519, 16679770774, 21767851261, 28628149140, 37899093699, 50427345906, 67324819329, 160271053137, 270418959297, 431339618961, 728414682073, 1341739076561, 2603393360841, 5070540418545, 9616206905361, 17540079266769, 30702211946673, 51683271869777, 83975931978793, 132213450495569, 202443610753657, 302459484256689, 442203574972449, 634269772099665, 894539565179169, 1243007095819281, 1704874490147833, 2312038112190161, 3105142640393385, 4136459386776945, 5473956026558385, 7207077040760529, 9454960484128017, 14963601160264401, 33266537977597425, 71986867934392497, 140041000763634297, 249057224673251345, 417012200783523881, 677060750076004497, 1097049810569011329, 1818981004342892241, 3133073830274926081, 5608509647747910001, 10312920238838113577, 19165848609356022289, 35488515242975515001, 64834202679764374097, 116211574230170388081, 203848698443298239697, 349690261861585347729]]
[26, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 36, 48, 68, 98, 140, 196, 268, 358, 468, 600, 756, 938, 1148, 1388, 1660, 1966, 2308, 2688, 3108, 3570, 4076, 4628, 5228, 5878, 6580, 7336, 15512, 23808, 32320, 41216, 50792, 61544, 74256, 90104, 110776, 138608, 176736, 229264, 301448, 399896, 532784, 710088, 943832, 1248352, 1640576, 2140320, 2770600, 3557960, 4532816, 5729816, 7188216, 8952272, 11071648, 15926624, 31422272, 63270656, 117385536, 199959200, 317553376, 477217664, 686658656, 954496864, 1290667520, 1707046016, 2218409984, 2843888544, 3609095840, 4549201408, 5713254944, 7170158432, 9016765120, 11388683264, 14474473664, 18534054560, 23922266208, 31118701184, 40765075936, 53711605088, 71074043264, 94303280512, 223441447936, 375202727168, 592853658624, 985832805120, 1784373488640, 3412253918080, 6579396971776, 12396515090048, 22514537527808, 39292203346944, 65996015372288, 107037832662016, 168256906098176, 257255413983872, 383799968894208, 560306803033984, 802436365115392, 1129835262757632, 1567081799085056, 2144918438518016, 2901893973972992, 3886594698164608, 5160723697603840, 6803398468171904, 8917189554314752, 11636629632385536, 15140199341037568, 23682429547296768, 51987890433273856, 111759844778143744, 216584507482681344, 383924291748505600, 640156543940347904, 1032722711753102336, 1656874090723301376, 2709618398587793408, 4590756041977643008, 8080904265710387200]]
[27, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 37, 49, 69, 99, 141, 197, 269, 359, 469, 601, 757, 939, 1149, 1389, 1661, 1967, 2309, 2689, 3109, 3571, 4077, 4629, 5229, 5879, 6581, 7337, 8149, 17197, 26369, 35763, 45549, 56025, 67689, 81327, 98117, 119749, 148561, 187691, 241245, 314481, 414009, 548007, 726453, 961373, 1267105, 1660579, 2161613, 2793225, 3581961, 4558239, 5756709, 7216629, 8982257, 11103259, 13635133, 19407844, 37792191, 75536538, 139612041, 237296736, 376273899, 564758166, 811672629, 1126914076, 1521762487, 2009515602, 2606460609, 3333333528, 4217463459, 5295854286, 6619521453, 8259476820, 10314841135, 12923662090, 16277127033, 20637983952, 26364123099, 33938425350, 44006152869, 57421343628, 75303874599, 99109079746, 130712049073, 308318031917, 515409846541, 807284827389, 1323066488913, 2354701127949, 4438660111101, 8472376131549, 15857991494161, 28676620098029, 49897059059469, 83623793405373, 135390323989233, 212505490334925, 324462838451517, 483426637214877, 704813536948977, 1007997060316077, 1417174506012045, 1962454370679421, 2681249714188817, 3620102589782157, 4837121478586365, 6405293802792285, 8417047025455185, 10990584739284333, 14278731298006157, 18481295904357181, 23862334343781809, 36920603864882389, 80082087562798709, 171072542454765701, 330328592942600721]]
[28, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 38, 50, 70, 100, 142, 198, 270, 360, 470, 602, 758, 940, 1150, 1390, 1662, 1968, 2310, 2690, 3110, 3572, 4078, 4630, 5230, 5880, 6582, 7338, 8150, 9020, 19000, 29108, 39444, 50180, 61616, 74252, 88876, 106668, 129320, 159172, 199364, 254004, 328352, 429020, 564188, 743836, 979992, 1286996, 1681780, 2184164, 2817168, 3607340, 4585100, 5785100, 7246600, 9013860, 11136548, 13670164, 16676480, 23500912, 45190208, 89674904, 165130864, 280071104, 443452080, 664807976, 954436256, 1323671696, 1785305056, 2354227256, 3048411152, 3890381536, 4909370576, 6144411336, 7648687040, 9495529136, 11786543744, 14662444504, 18317280944, 23016876032, 29122425328, 37120363880, 47659776480, 61598812880, 80061772832, 104508747128, 136819940944, 179397065504, 421336666688, 701383094496, 1089658593632, 1761666225664, 3084798914816, 5733098588672, 10832642217376, 20140567933024, 36261470195392, 62905726146720, 105195329647328, 170024112343616, 266480999496576, 406347465665728, 604684061765920, 880526443529120, 1257719713871680, 1765932487620192, 2441910839326816, 3331059866197120, 4489480572826112, 5986646910338432, 7908988277743776, 10364754603160800, 13490694432345024, 17461284061415968]]
[29, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 39, 51, 71, 101, 143, 199, 271, 361, 471, 603, 759, 941, 1151, 1391, 1663, 1969, 2311, 2691, 3111, 3573, 4079, 4631, 5231, 5881, 6583, 7339, 8151, 9021, 9951, 20925, 32031, 43371, 55119, 67577, 81247, 96919, 115775, 139509, 170463, 211779, 267567, 343089, 444959, 581359, 762271, 999725, 1308063, 1704219, 2208015, 2842473, 3634143, 4613447, 5815039, 7278181, 9047135, 11171571, 13706991, 16715169, 20264607, 28288926, 53742933, 105900156, 194303475, 328865178, 519981673, 778676440, 1116794535, 1547285910, 2084633757, 2745508788, 3549761595, 4521903762, 5693274993, 7105148944, 8813095471, 10892992398, 13449166437, 16625241324, 20618382339, 25697750922, 32228121849, 40699769160, 51765896503, 66289073542, 85398343341, 110558886948, 143656371531, 187098368130, 243935505153, 570557171457, 946038069945, 1458649499553, 2328193264617, 4013715109761, 7356144501393, 13758632896321, 25408096619825, 45542289783681, 78767676516297, 131434505227233, 212076919404249, 331927848023553, 505521089098337, 751396873962625, 1092932942452961, 1559331744041473, 2186807198843481, 3020033450397729, 4113945884347209]]
[30, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 40, 52, 72, 102, 144, 200, 272, 362, 472, 604, 760, 942, 1152, 1392, 1664, 1970, 2312, 2692, 3112, 3574, 4080, 4632, 5232, 5882, 6584, 7340, 8152, 9022, 9952, 10944, 22976, 35144, 47552, 60376, 73920, 88688, 105472, 125456, 150336, 182456, 224960, 281960, 358720, 461856, 599552, 781792, 1020608, 1330344, 1727936, 2233208, 2869184, 3662416, 4643328, 5846576, 7311424, 9082136, 11208384, 13745672, 16755776, 20307200, 24475648, 33863168, 63588096, 124443712, 227518208, 384303488, 606818816, 907762944, 1300718080, 1800443008, 2423311616, 3187977792, 4116378880, 5235228416, 6578195456, 8189023232, 10125904896, 12467509504, 15321137920, 18833586752, 23205409536, 28709388928, 35714172416, 44714177792, 56367044096, 71540089728, 91367442688, 117319729216, 151288447232, 195687410688, 253573931008, 328792702976, 766005493760, 1265398304768, 1937325258752, 3055206093824, 5188764995584, 9380191795200, 17366444433408, 31851755218944, 56835338645504, 98000365868032, 163171536812032, 262850155460608, 410837677154304, 624961535451136]]
[31, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 41, 53, 73, 103, 145, 201, 273, 363, 473, 605, 761, 943, 1153, 1393, 1665, 1971, 2313, 2693, 3113, 3575, 4081, 4633, 5233, 5883, 6585, 7341, 8153, 9023, 9953, 10945, 12001, 25157, 38453, 51995, 65961, 80657, 96589, 114551, 135729, 161821, 195173, 238931, 297209, 375273, 479741, 618799, 802433, 1042677, 1353877, 1752971, 2259785, 2897345, 3692205, 4674791, 5879761, 7346381, 9118917, 11247043, 13786265, 16798361, 20351837, 24522399, 29393441, 40323624, 74875163, 145554814, 265191389, 447053828, 704984311, 1053560090, 1508307449, 2086005152, 2805133683, 3686551286, 4754509045, 6038155772, 7573730063, 9407692306, 11601114449, 14235720728, 17422059083, 21310381422, 26104921997, 32082387700, 39615612839, 49203484682, 61508415529, 77402823056, 98026283939, 124855247078, 159787432869, 205243304684, 264287278783, 340771640066, 439506454145, 1020074487949, 1679220980437, 2554014909149, 3982407168433, 6667028101293, 11891435488405, 21792534975805, 39693861349505]]
[32, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 42, 54, 74, 104, 146, 202, 274, 364, 474, 606, 762, 944, 1154, 1394, 1666, 1972, 2314, 2694, 3114, 3576, 4082, 4634, 5234, 5884, 6586, 7342, 8154, 9024, 9954, 10946, 12002, 13124, 27472, 41964, 56708, 71884, 87800, 104964, 124172, 146612, 173984, 208636, 253716, 313340, 392776, 498644, 639132, 824228, 1065968, 1378700, 1779364, 2287788, 2927000, 3723556, 4707884, 5914644, 7383104, 9157532, 11287604, 13828828, 16842984, 20398580, 24571324, 29444612, 35110032, 47779520, 87765968, 169501352, 307768480, 517828880, 815565920, 1217656888, 1741797488, 2407016160, 3234134576, 4246455368, 5470789376, 6938973232, 8690074688, 10773538520, 13253590864, 16215295232, 19772739984, 24079935464, 29345110112, 35849219408, 43969620256, 54210017144, 67237955888, 83931326752, 105435542000, 133233274248, 169228882112, 215849909360, 276168323840, 354044463640, 454296981008, 582902420288, 1347991143424, 2211725253568]]
[33, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 43, 55, 75, 105, 147, 203, 275, 365, 475, 607, 763, 945, 1155, 1395, 1667, 1973, 2315, 2695, 3115, 3577, 4083, 4635, 5235, 5885, 6587, 7343, 8155, 9025, 9955, 10947, 12003, 13125, 14315, 29925, 45683, 61699, 78155, 95361, 113827, 134351, 158123, 186845, 222867, 269339, 330379, 411257, 518595, 660583, 847211, 1090517, 1404851, 1807155, 2317259, 2958193, 3756515, 4742655, 5951275, 7421645, 9198035, 11330123, 13873419, 16889705, 20447491, 24622487, 29498091, 35165893, 41726195, 56349874, 102435361, 196570704, 355725239, 597387854, 939720677, 1401741964, 2003561691, 2766707306, 3714596041, 4873234888, 6272260575, 7946470406, 9938041421, 12299690756, 15099095107, 18424962594, 22395236849, 27168011584, 32955844999, 40044287934, 48815578421, 59778609020, 73606442795, 91182839770, 113659458969, 142525622456, 179692767919, 227595976054, 289315239069]]
[34, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 44, 56, 76, 106, 148, 204, 276, 366, 476, 608, 764, 946, 1156, 1396, 1668, 1974, 2316, 2696, 3116, 3578, 4084, 4636, 5236, 5886, 6588, 7344, 8156, 9026, 9956, 10948, 12004, 13126, 14316, 15576, 32520, 49616, 66976, 84784, 103352, 123192, 145104, 170280, 200424, 237888, 285824, 348352, 430744, 539624, 683184, 871416, 1116360, 1432368, 1836384, 2348240, 2990968, 3791128, 4779152, 5989704, 7462056, 9240480, 11374656, 13920096, 16938584, 20498632, 24675952, 29553944, 35224200, 41787024, 49351968, 66164064, 119071872, 227070592, 409568896, 686538144, 1078677216, 1607606784, 2296116576, 3168503136, 4251054528, 5572763136, 7166378944, 9069954208, 11329077024, 14000046720, 17154309024, 20884544352, 25312889088, 30601868160, 36968728320, 44703986080, 54195143008, 65956674816, 80667570144, 99217880928]]
[35, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 45, 57, 77, 107, 149, 205, 277, 367, 477, 609, 765, 947, 1157, 1397, 1669, 1975, 2317, 2697, 3117, 3579, 4085, 4637, 5237, 5887, 6589, 7345, 8157, 9027, 9957, 10949, 12005, 13127, 14317, 15577, 16909, 35261, 53769, 72547, 91781, 111785, 133073, 156447, 183101, 214741, 253721, 303195, 367285, 451265, 561761, 706967, 896877, 1143533, 1461289, 1867091, 2380773, 3025369, 3827441, 4817423, 6029981, 7504389, 9284921, 11421259, 13968917, 16989681, 20552065, 24731783, 29612237, 35285021, 41850441, 49418051, 58107205, 77362412, 137878391, 261329954, 469839345, 786137000, 1233738115, 1837148894, 2622126077, 3616027300, 4848308783, 6351251546, 8161028585, 10319263968, 12875281403, 15889295254, 19436862005, 23614985564, 28550356327, 34410302354, 41417142113]]
[36, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 46, 58, 78, 108, 150, 206, 278, 368, 478, 610, 766, 948, 1158, 1398, 1670, 1976, 2318, 2698, 3118, 3580, 4086, 4638, 5238, 5888, 6590, 7346, 8158, 9028, 9958, 10950, 12006, 13128, 14318, 15578, 16910, 18316, 38152, 58148, 78420, 99156, 120672, 143484, 168396, 196604, 229816, 270388, 321476, 387204, 472848, 585036, 731964, 923628, 1172072, 1491652, 1899316, 2414900, 3061440, 3865500, 4857516, 6072156, 7548696, 9331412, 11469988, 14019940, 17043056, 20607852, 24790044, 29673036, 35348424, 41916516, 49486868, 58178836, 68122144, 90096784, 159072864, 299699832, 537110352, 897093216, 1406282256, 2092375176, 2984405952, 4113108400, 5511427456, 7215259416, 9264533616, 11704786560, 14589426096, 17982938664]]
[37, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 47, 59, 79, 109, 151, 207, 279, 369, 479, 611, 767, 949, 1159, 1399, 1671, 1977, 2319, 2699, 3119, 3581, 4087, 4639, 5239, 5889, 6591, 7347, 8159, 9029, 9959, 10951, 12007, 13129, 14319, 15579, 16911, 18317, 19799, 41197, 62759, 84603, 106919, 130025, 154439, 180967, 210807, 245669, 287911, 340691, 408135, 495521, 609479, 758207, 951703, 1202013, 1523495, 1933099, 2450663, 3099225, 3905351, 4899479, 6116279, 7595029, 9380007, 11520899, 14073223, 17098769, 20666055, 24850799, 29736407, 35414477, 41985319, 49558491, 58253351, 68199625, 79537991, 104531206, 182889005, 342554276, 611990779, 1020368834, 1597767201, 2375405120, 3385928207, 4663785854, 6245756725]]
[38, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 48, 60, 80, 110, 152, 208, 280, 370, 480, 612, 768, 950, 1160, 1400, 1672, 1978, 2320, 2700, 3120, 3582, 4088, 4640, 5240, 5890, 6592, 7348, 8160, 9030, 9960, 10952, 12008, 13130, 14320, 15580, 16912, 18318, 19800, 21360, 44400, 67608, 91104, 115080, 139856, 165952, 194176, 225728, 262320, 306312, 360864, 430104, 519312, 635120, 785728, 981136, 1233392, 1556856, 1968480, 2488104, 3138768, 3947040, 4943360, 6162400, 7643440, 9430760, 11574048, 14128824, 17156880, 20726736, 24914112, 29802416, 35483248, 42056920, 49632992, 58330824, 68280144, 79621632, 92507520, 120842496, 209577024, 390291264, 695125824, 1156980864]]
[39, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 49, 61, 81, 111, 153, 209, 281, 371, 481, 613, 769, 951, 1161, 1401, 1673, 1979, 2321, 2701, 3121, 3583, 4089, 4641, 5241, 5891, 6593, 7349, 8161, 9031, 9961, 10953, 12009, 13131, 14321, 15581, 16913, 18319, 19801, 21361, 23001, 47765, 72701, 97931, 123649, 150177, 178037, 208039, 241385, 279789, 325613, 382019, 453137, 544249, 661989, 814559, 1011961, 1266245, 1591773, 2005499, 2527265, 3180113, 3990613, 4989207, 6210569, 7693981, 9483725, 11629491, 14186801, 17217449, 20789957, 24980047, 29871129, 35554805, 42131389, 49710443, 58411329, 68363777, 79708469, 92597639, 107195689]]
[40, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 50, 62, 82, 112, 154, 210, 282, 372, 482, 614, 770, 952, 1162, 1402, 1674, 1980, 2322, 2702, 3122, 3584, 4090, 4642, 5242, 5892, 6594, 7350, 8162, 9032, 9962, 10954, 12010, 13132, 14322, 15582, 16914, 18320, 19802, 21362, 23002, 24724, 51296, 78044, 105092, 132636, 161000, 190708, 222572, 257796, 298096, 345836, 404180, 477260, 570360, 690116, 844732, 1044212, 1300608, 1628284, 2044196, 2568188, 3223304, 4036116, 5037068, 6260836, 7746704, 9538956, 11687284, 14247212, 17280536, 20855780, 25048668, 29942612, 35629216, 42208796, 49790916, 58494940]]
[41, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 51, 63, 83, 113, 155, 211, 283, 373, 483, 615, 771, 953, 1163, 1403, 1675, 1981, 2323, 2703, 3123, 3585, 4091, 4643, 5243, 5893, 6595, 7351, 8163, 9033, 9963, 10955, 12011, 13133, 14323, 15583, 16915, 18321, 19803, 21363, 23003, 24725, 26531, 54997, 83643, 112595, 142051, 172337, 203979, 237791, 274979, 317261, 367003, 427371, 502499, 597673, 719531, 876279, 1077923, 1336517, 1666427, 2084611, 2610915, 3268385, 4083595, 5086991, 6313251, 7801661, 9596507, 11747483, 14310115, 17346201, 20924267, 25120039, 30016931]]
[42, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 52, 64, 84, 114, 156, 212, 284, 374, 484, 616, 772, 954, 1164, 1404, 1676, 1982, 2324, 2704, 3124, 3586, 4092, 4644, 5244, 5894, 6596, 7352, 8164, 9034, 9964, 10956, 12012, 13134, 14324, 15584, 16916, 18322, 19804, 21364, 23004, 24726, 26532, 28424, 58872, 89504, 120448, 151904, 184200, 217864, 253712, 292952, 337304, 389136, 451616, 528880, 626216, 750264, 909232, 1113128, 1374008, 1706240, 2126784, 2655488, 3315400, 4133096, 5139024, 6367864, 7858904, 9656432, 11810144, 14375568]]
[43, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 53, 65, 85, 115, 157, 213, 285, 375, 485, 617, 773, 955, 1165, 1405, 1677, 1983, 2325, 2705, 3125, 3587, 4093, 4645, 5245, 5895, 6597, 7353, 8165, 9035, 9965, 10957, 12013, 13135, 14325, 15585, 16917, 18323, 19805, 21365, 23005, 24727, 26533, 28425, 30405, 62925, 95633, 128659, 162205, 196601, 232377, 270351, 311733, 358245, 412257, 476939, 556429, 656017, 782345, 943623, 1149861, 1413117, 1747761, 2170755, 2701949, 3364393, 4184665, 5193215, 6424725]]
[44, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 54, 66, 86, 116, 158, 214, 286, 376, 486, 618, 774, 956, 1166, 1406, 1678, 1984, 2326, 2706, 3126, 3588, 4094, 4646, 5246, 5896, 6598, 7354, 8166, 9036, 9966, 10958, 12014, 13136, 14326, 15586, 16918, 18324, 19806, 21366, 23006, 24728, 26534, 28426, 30406, 32476, 67160, 102036, 137236, 172964, 209552, 247532, 287724, 331340, 380104, 436388, 503364, 585172, 687104, 815804, 979484, 1188156, 1453880, 1791028, 2216564, 2750340]]
[45, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 55, 67, 87, 117, 159, 215, 287, 377, 487, 619, 775, 957, 1167, 1407, 1679, 1985, 2327, 2707, 3127, 3589, 4095, 4647, 5247, 5897, 6599, 7355, 8167, 9037, 9967, 10959, 12015, 13137, 14327, 15587, 16919, 18325, 19807, 21367, 23007, 24729, 26535, 28427, 30407, 32477, 34639, 71581, 108719, 146187, 184191, 223065, 263343, 305847, 351791, 402901, 461551, 530915, 615135, 719505, 850671, 1016847, 1228047]]
[46, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 56, 68, 88, 118, 160, 216, 288, 378, 488, 620, 776, 958, 1168, 1408, 1680, 1986, 2328, 2708, 3128, 3590, 4096, 4648, 5248, 5898, 6600, 7356, 8168, 9038, 9968, 10960, 12016, 13138, 14328, 15588, 16920, 18326, 19808, 21368, 23008, 24730, 26536, 28428, 30408, 32478, 34640, 36896, 76192, 115688, 155520, 195896, 237152, 279824, 324736, 373104, 426656, 487768, 559616, 646344]]
[47, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 57, 69, 89, 119, 161, 217, 289, 379, 489, 621, 777, 959, 1169, 1409, 1681, 1987, 2329, 2709, 3129, 3591, 4097, 4649, 5249, 5899, 6601, 7357, 8169, 9039, 9969, 10961, 12017, 13139, 14329, 15589, 16921, 18327, 19809, 21369, 23009, 24731, 26537, 28429, 30409, 32479, 34641, 36897, 39249, 80997, 122949, 165243, 208089, 251825, 296989, 344407, 395297]]
[48, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 58, 70, 90, 120, 162, 218, 290, 380, 490, 622, 778, 960, 1170, 1410, 1682, 1988, 2330, 2710, 3130, 3592, 4098, 4650, 5250, 5900, 6602, 7358, 8170, 9040, 9970, 10962, 12018, 13140, 14330, 15590, 16922, 18328, 19810, 21370, 23010, 24732, 26538, 28430, 30410, 32480, 34642, 36898, 39250, 41700, 86000, 130508, 175364, 220780]]
[49, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 59, 71, 91, 121, 163, 219, 291, 381, 491, 623, 779, 961, 1171, 1411, 1683, 1989, 2331, 2711, 3131, 3593, 4099, 4651, 5251, 5901, 6603, 7359, 8171, 9041, 9971, 10963, 12019, 13141, 14331, 15591, 16923, 18329, 19811, 21371, 23011, 24733, 26539, 28431, 30411, 32481, 34643, 36899, 39251, 41701, 44251]]
[50, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 60, 72, 92, 122, 164, 220, 292, 382, 492, 624, 780, 962, 1172, 1412, 1684, 1990, 2332, 2712, 3132, 3594, 4100, 4652, 5252, 5902, 6604, 7360, 8172, 9042, 9972, 10964, 12020, 13142, 14332, 15592, 16924, 18330, 19812, 21372, 23012, 24734, 26540, 28432, 30412, 32482, 34644, 36900]]