2016年7月19日火曜日

160719

Ruby


Triangular array associated with little Schroeder numbers

オンライン整数列大辞典の
A144944(http://oeis.org/A144944/list)
に載っているが、自分でも求めてみた。

n = 20
# 0行目
a = [0, 1]
p [0, a[1..-1]]
n.times{|i|
  b = [0]
  (0..i).each{|j| b[j + 1] = a[j] + a[j + 1] + b[j]}
  b << b[-1]
  a = b
  p [i + 1, a[1..-1]]
}

出力結果
[0, [1]]
[1, [1, 1]]
[2, [1, 3, 3]]
[3, [1, 5, 11, 11]]
[4, [1, 7, 23, 45, 45]]
[5, [1, 9, 39, 107, 197, 197]]
[6, [1, 11, 59, 205, 509, 903, 903]]
[7, [1, 13, 83, 347, 1061, 2473, 4279, 4279]]
[8, [1, 15, 111, 541, 1949, 5483, 12235, 20793, 20793]]
[9, [1, 17, 143, 795, 3285, 10717, 28435, 61463, 103049, 103049]]
[10, [1, 19, 179, 1117, 5197, 19199, 58351, 148249, 312761, 518859, 518859]]
[11, [1, 21, 219, 1515, 7829, 32225, 109775, 316375, 777385, 1609005, 2646723, 2646723]]
[12, [1, 23, 263, 1997, 11341, 51395, 193395, 619545, 1713305, 4099695, 8355423, 13648869, 13648869]]
[13, [1, 25, 311, 2571, 15909, 78645, 323435, 1136375, 3469225, 9282225, 21737343, 43741635, 71039373, 71039373]]
[14, [1, 27, 363, 3245, 21725, 116279, 518359, 1978169, 6583769, 19335219, 50354787, 115833765, 230614773, 372693519, 372693519]]
[15, [1, 29, 419, 4027, 28997, 167001, 801639, 3298167, 11860105, 37779093, 107469099, 273657651, 620106189, 1223414481, 1968801519, 1968801519]]
[16, [1, 31, 479, 4925, 37949, 233947, 1202587, 5302393, 20460665, 70099863, 215348055, 596474805, 1490238645, 3333759315, 6525975315, 10463578353, 10463578353]]
[17, [1, 33, 543, 5947, 48821, 320717, 1757251, 8262231, 34025289, 124585817, 410033735, 1221856595, 3308570045, 8132568005, 17992302635, 34981856303, 55909013009, 55909013009]]
[18, [1, 35, 611, 7101, 61869, 431407, 2509375, 12528857, 54816377, 213427483, 748047035, 2379937365, 6910364005, 18351502055, 44476372695, 97450531633, 188341400945, 300159426963, 300159426963]]
[19, [1, 37, 683, 8395, 77365, 570641, 3511423, 18549655, 85894889, 354138749, 1315613267, 4443597667, 13733899037, 38995765097, 101823639847, 243750544175, 529542476753, 1018043304661, 1618362158587, 1618362158587]]
[20, [1, 39, 759, 9837, 95597, 743603, 4825667, 26886745, 131331289, 571364927, 2241116943, 8000327877, 26177824581, 78907488715, 219726893659, 565301077681, 1338594098609, 2886179880023, 5522585343271, 8759309660445, 8759309660445]]

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