200723

PARI


A307883 とA307884

diagonal of the rational function R(r, k) = r / ((1-r*x)*(1-r*y) + r-1 - (k+r-1)*r*x*y)

がr (≠0) の値に依存しないことは、以下のように展開すれば確認できる。

R(r, k)

= r / ((1-r*x-r*y+r^2*x*y) + r-1 - (k+r-1)*r*x*y)

= r / (r * (1-x-y-(k-1)*x*y))

= 1 / ((1-x)*(1-y) - k*x*y)

= R(1, k)

実際計算でも確かめてみた。

(00:00) gp > N=10;
(00:00) gp > diag(n, expr, var=variables(expr)) = {
  my(a=vector(n));
  for(i=1, #var, expr=taylor(expr, var[#var-i+1], n));
  for(j=1, n, a[j]=expr;
    for(i=1, #var, a[j]=polcoeff(a[j], j-1)));
  return(a);
};
(00:00) gp > R(r, k) = r/((1-r*x)*(1-r*y)+r-1-(k+r-1)*r*x*y);
(00:00) gp > for(k=-10, 10, for(r=-5, 5, if(r!=0, print("(r,k) = (", r, ",", k, ") ", diag(N, R(r, k))))))
(r,k) = (-5,-10) [1, -9, 61, -189, -2559, 59751, -727859, 5968611, -23658239, -239767209]
(r,k) = (-4,-10) [1, -9, 61, -189, -2559, 59751, -727859, 5968611, -23658239, -239767209]
(r,k) = (-3,-10) [1, -9, 61, -189, -2559, 59751, -727859, 5968611, -23658239, -239767209]
(r,k) = (-2,-10) [1, -9, 61, -189, -2559, 59751, -727859, 5968611, -23658239, -239767209]
(r,k) = (-1,-10) [1, -9, 61, -189, -2559, 59751, -727859, 5968611, -23658239, -239767209]
(r,k) = (1,-10) [1, -9, 61, -189, -2559, 59751, -727859, 5968611, -23658239, -239767209]
(r,k) = (2,-10) [1, -9, 61, -189, -2559, 59751, -727859, 5968611, -23658239, -239767209]
(r,k) = (3,-10) [1, -9, 61, -189, -2559, 59751, -727859, 5968611, -23658239, -239767209]
(r,k) = (4,-10) [1, -9, 61, -189, -2559, 59751, -727859, 5968611, -23658239, -239767209]
(r,k) = (5,-10) [1, -9, 61, -189, -2559, 59751, -727859, 5968611, -23658239, -239767209]
(r,k) = (-5,-9) [1, -8, 46, -80, -2330, 39952, -391796, 2396512, -1665530, -187855280]
(r,k) = (-4,-9) [1, -8, 46, -80, -2330, 39952, -391796, 2396512, -1665530, -187855280]
(r,k) = (-3,-9) [1, -8, 46, -80, -2330, 39952, -391796, 2396512, -1665530, -187855280]
(r,k) = (-2,-9) [1, -8, 46, -80, -2330, 39952, -391796, 2396512, -1665530, -187855280]
(r,k) = (-1,-9) [1, -8, 46, -80, -2330, 39952, -391796, 2396512, -1665530, -187855280]
(r,k) = (1,-9) [1, -8, 46, -80, -2330, 39952, -391796, 2396512, -1665530, -187855280]
(r,k) = (2,-9) [1, -8, 46, -80, -2330, 39952, -391796, 2396512, -1665530, -187855280]
(r,k) = (3,-9) [1, -8, 46, -80, -2330, 39952, -391796, 2396512, -1665530, -187855280]
(r,k) = (4,-9) [1, -8, 46, -80, -2330, 39952, -391796, 2396512, -1665530, -187855280]
(r,k) = (5,-9) [1, -8, 46, -80, -2330, 39952, -391796, 2396512, -1665530, -187855280]
(r,k) = (-5,-8) [1, -7, 33, -7, -1919, 24633, -186591, 715449, 3834369, -102211207]
(r,k) = (-4,-8) [1, -7, 33, -7, -1919, 24633, -186591, 715449, 3834369, -102211207]
(r,k) = (-3,-8) [1, -7, 33, -7, -1919, 24633, -186591, 715449, 3834369, -102211207]
(r,k) = (-2,-8) [1, -7, 33, -7, -1919, 24633, -186591, 715449, 3834369, -102211207]
(r,k) = (-1,-8) [1, -7, 33, -7, -1919, 24633, -186591, 715449, 3834369, -102211207]
(r,k) = (1,-8) [1, -7, 33, -7, -1919, 24633, -186591, 715449, 3834369, -102211207]
(r,k) = (2,-8) [1, -7, 33, -7, -1919, 24633, -186591, 715449, 3834369, -102211207]
(r,k) = (3,-8) [1, -7, 33, -7, -1919, 24633, -186591, 715449, 3834369, -102211207]
(r,k) = (4,-8) [1, -7, 33, -7, -1919, 24633, -186591, 715449, 3834369, -102211207]
(r,k) = (5,-8) [1, -7, 33, -7, -1919, 24633, -186591, 715449, 3834369, -102211207]
(r,k) = (-5,-7) [1, -6, 22, 36, -1434, 13644, -73604, 71688, 3315334, -41652036]
(r,k) = (-4,-7) [1, -6, 22, 36, -1434, 13644, -73604, 71688, 3315334, -41652036]
(r,k) = (-3,-7) [1, -6, 22, 36, -1434, 13644, -73604, 71688, 3315334, -41652036]
(r,k) = (-2,-7) [1, -6, 22, 36, -1434, 13644, -73604, 71688, 3315334, -41652036]
(r,k) = (-1,-7) [1, -6, 22, 36, -1434, 13644, -73604, 71688, 3315334, -41652036]
(r,k) = (1,-7) [1, -6, 22, 36, -1434, 13644, -73604, 71688, 3315334, -41652036]
(r,k) = (2,-7) [1, -6, 22, 36, -1434, 13644, -73604, 71688, 3315334, -41652036]
(r,k) = (3,-7) [1, -6, 22, 36, -1434, 13644, -73604, 71688, 3315334, -41652036]
(r,k) = (4,-7) [1, -6, 22, 36, -1434, 13644, -73604, 71688, 3315334, -41652036]
(r,k) = (5,-7) [1, -6, 22, 36, -1434, 13644, -73604, 71688, 3315334, -41652036]
(r,k) = (-5,-6) [1, -5, 13, 55, -959, 6475, -20195, -84425, 1657345, -11975525]
(r,k) = (-4,-6) [1, -5, 13, 55, -959, 6475, -20195, -84425, 1657345, -11975525]
(r,k) = (-3,-6) [1, -5, 13, 55, -959, 6475, -20195, -84425, 1657345, -11975525]
(r,k) = (-2,-6) [1, -5, 13, 55, -959, 6475, -20195, -84425, 1657345, -11975525]
(r,k) = (-1,-6) [1, -5, 13, 55, -959, 6475, -20195, -84425, 1657345, -11975525]
(r,k) = (1,-6) [1, -5, 13, 55, -959, 6475, -20195, -84425, 1657345, -11975525]
(r,k) = (2,-6) [1, -5, 13, 55, -959, 6475, -20195, -84425, 1657345, -11975525]
(r,k) = (3,-6) [1, -5, 13, 55, -959, 6475, -20195, -84425, 1657345, -11975525]
(r,k) = (4,-6) [1, -5, 13, 55, -959, 6475, -20195, -84425, 1657345, -11975525]
(r,k) = (5,-6) [1, -5, 13, 55, -959, 6475, -20195, -84425, 1657345, -11975525]
(r,k) = (-5,-5) [1, -4, 6, 56, -554, 2376, -804, -67344, 530406, -1852504]
(r,k) = (-4,-5) [1, -4, 6, 56, -554, 2376, -804, -67344, 530406, -1852504]
(r,k) = (-3,-5) [1, -4, 6, 56, -554, 2376, -804, -67344, 530406, -1852504]
(r,k) = (-2,-5) [1, -4, 6, 56, -554, 2376, -804, -67344, 530406, -1852504]
(r,k) = (-1,-5) [1, -4, 6, 56, -554, 2376, -804, -67344, 530406, -1852504]
(r,k) = (1,-5) [1, -4, 6, 56, -554, 2376, -804, -67344, 530406, -1852504]
(r,k) = (2,-5) [1, -4, 6, 56, -554, 2376, -804, -67344, 530406, -1852504]
(r,k) = (3,-5) [1, -4, 6, 56, -554, 2376, -804, -67344, 530406, -1852504]
(r,k) = (4,-5) [1, -4, 6, 56, -554, 2376, -804, -67344, 530406, -1852504]
(r,k) = (5,-5) [1, -4, 6, 56, -554, 2376, -804, -67344, 530406, -1852504]
(r,k) = (-5,-4) [1, -3, 1, 45, -255, 477, 2689, -25203, 82945, 90045]
(r,k) = (-4,-4) [1, -3, 1, 45, -255, 477, 2689, -25203, 82945, 90045]
(r,k) = (-3,-4) [1, -3, 1, 45, -255, 477, 2689, -25203, 82945, 90045]
(r,k) = (-2,-4) [1, -3, 1, 45, -255, 477, 2689, -25203, 82945, 90045]
(r,k) = (-1,-4) [1, -3, 1, 45, -255, 477, 2689, -25203, 82945, 90045]
(r,k) = (1,-4) [1, -3, 1, 45, -255, 477, 2689, -25203, 82945, 90045]
(r,k) = (2,-4) [1, -3, 1, 45, -255, 477, 2689, -25203, 82945, 90045]
(r,k) = (3,-4) [1, -3, 1, 45, -255, 477, 2689, -25203, 82945, 90045]
(r,k) = (4,-4) [1, -3, 1, 45, -255, 477, 2689, -25203, 82945, 90045]
(r,k) = (5,-4) [1, -3, 1, 45, -255, 477, 2689, -25203, 82945, 90045]
(r,k) = (-5,-3) [1, -2, -2, 28, -74, -92, 1324, -3656, -4826, 70228]
(r,k) = (-4,-3) [1, -2, -2, 28, -74, -92, 1324, -3656, -4826, 70228]
(r,k) = (-3,-3) [1, -2, -2, 28, -74, -92, 1324, -3656, -4826, 70228]
(r,k) = (-2,-3) [1, -2, -2, 28, -74, -92, 1324, -3656, -4826, 70228]
(r,k) = (-1,-3) [1, -2, -2, 28, -74, -92, 1324, -3656, -4826, 70228]
(r,k) = (1,-3) [1, -2, -2, 28, -74, -92, 1324, -3656, -4826, 70228]
(r,k) = (2,-3) [1, -2, -2, 28, -74, -92, 1324, -3656, -4826, 70228]
(r,k) = (3,-3) [1, -2, -2, 28, -74, -92, 1324, -3656, -4826, 70228]
(r,k) = (4,-3) [1, -2, -2, 28, -74, -92, 1324, -3656, -4826, 70228]
(r,k) = (5,-3) [1, -2, -2, 28, -74, -92, 1324, -3656, -4826, 70228]
(r,k) = (-5,-2) [1, -1, -3, 11, 1, -81, 141, 363, -1791, 479]
(r,k) = (-4,-2) [1, -1, -3, 11, 1, -81, 141, 363, -1791, 479]
(r,k) = (-3,-2) [1, -1, -3, 11, 1, -81, 141, 363, -1791, 479]
(r,k) = (-2,-2) [1, -1, -3, 11, 1, -81, 141, 363, -1791, 479]
(r,k) = (-1,-2) [1, -1, -3, 11, 1, -81, 141, 363, -1791, 479]
(r,k) = (1,-2) [1, -1, -3, 11, 1, -81, 141, 363, -1791, 479]
(r,k) = (2,-2) [1, -1, -3, 11, 1, -81, 141, 363, -1791, 479]
(r,k) = (3,-2) [1, -1, -3, 11, 1, -81, 141, 363, -1791, 479]
(r,k) = (4,-2) [1, -1, -3, 11, 1, -81, 141, 363, -1791, 479]
(r,k) = (5,-2) [1, -1, -3, 11, 1, -81, 141, 363, -1791, 479]
(r,k) = (-5,-1) [1, 0, -2, 0, 6, 0, -20, 0, 70, 0]
(r,k) = (-4,-1) [1, 0, -2, 0, 6, 0, -20, 0, 70, 0]
(r,k) = (-3,-1) [1, 0, -2, 0, 6, 0, -20, 0, 70, 0]
(r,k) = (-2,-1) [1, 0, -2, 0, 6, 0, -20, 0, 70, 0]
(r,k) = (-1,-1) [1, 0, -2, 0, 6, 0, -20, 0, 70, 0]
(r,k) = (1,-1) [1, 0, -2, 0, 6, 0, -20, 0, 70, 0]
(r,k) = (2,-1) [1, 0, -2, 0, 6, 0, -20, 0, 70, 0]
(r,k) = (3,-1) [1, 0, -2, 0, 6, 0, -20, 0, 70, 0]
(r,k) = (4,-1) [1, 0, -2, 0, 6, 0, -20, 0, 70, 0]
(r,k) = (5,-1) [1, 0, -2, 0, 6, 0, -20, 0, 70, 0]
(r,k) = (-5,0) [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
(r,k) = (-4,0) [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
(r,k) = (-3,0) [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
(r,k) = (-2,0) [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
(r,k) = (-1,0) [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
(r,k) = (1,0) [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
(r,k) = (2,0) [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
(r,k) = (3,0) [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
(r,k) = (4,0) [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
(r,k) = (5,0) [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
(r,k) = (-5,1) [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620]
(r,k) = (-4,1) [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620]
(r,k) = (-3,1) [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620]
(r,k) = (-2,1) [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620]
(r,k) = (-1,1) [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620]
(r,k) = (1,1) [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620]
(r,k) = (2,1) [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620]
(r,k) = (3,1) [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620]
(r,k) = (4,1) [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620]
(r,k) = (5,1) [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620]
(r,k) = (-5,2) [1, 3, 13, 63, 321, 1683, 8989, 48639, 265729, 1462563]
(r,k) = (-4,2) [1, 3, 13, 63, 321, 1683, 8989, 48639, 265729, 1462563]
(r,k) = (-3,2) [1, 3, 13, 63, 321, 1683, 8989, 48639, 265729, 1462563]
(r,k) = (-2,2) [1, 3, 13, 63, 321, 1683, 8989, 48639, 265729, 1462563]
(r,k) = (-1,2) [1, 3, 13, 63, 321, 1683, 8989, 48639, 265729, 1462563]
(r,k) = (1,2) [1, 3, 13, 63, 321, 1683, 8989, 48639, 265729, 1462563]
(r,k) = (2,2) [1, 3, 13, 63, 321, 1683, 8989, 48639, 265729, 1462563]
(r,k) = (3,2) [1, 3, 13, 63, 321, 1683, 8989, 48639, 265729, 1462563]
(r,k) = (4,2) [1, 3, 13, 63, 321, 1683, 8989, 48639, 265729, 1462563]
(r,k) = (5,2) [1, 3, 13, 63, 321, 1683, 8989, 48639, 265729, 1462563]
(r,k) = (-5,3) [1, 4, 22, 136, 886, 5944, 40636, 281488, 1968934, 13875544]
(r,k) = (-4,3) [1, 4, 22, 136, 886, 5944, 40636, 281488, 1968934, 13875544]
(r,k) = (-3,3) [1, 4, 22, 136, 886, 5944, 40636, 281488, 1968934, 13875544]
(r,k) = (-2,3) [1, 4, 22, 136, 886, 5944, 40636, 281488, 1968934, 13875544]
(r,k) = (-1,3) [1, 4, 22, 136, 886, 5944, 40636, 281488, 1968934, 13875544]
(r,k) = (1,3) [1, 4, 22, 136, 886, 5944, 40636, 281488, 1968934, 13875544]
(r,k) = (2,3) [1, 4, 22, 136, 886, 5944, 40636, 281488, 1968934, 13875544]
(r,k) = (3,3) [1, 4, 22, 136, 886, 5944, 40636, 281488, 1968934, 13875544]
(r,k) = (4,3) [1, 4, 22, 136, 886, 5944, 40636, 281488, 1968934, 13875544]
(r,k) = (5,3) [1, 4, 22, 136, 886, 5944, 40636, 281488, 1968934, 13875544]
(r,k) = (-5,4) [1, 5, 33, 245, 1921, 15525, 127905, 1067925, 9004545, 76499525]
(r,k) = (-4,4) [1, 5, 33, 245, 1921, 15525, 127905, 1067925, 9004545, 76499525]
(r,k) = (-3,4) [1, 5, 33, 245, 1921, 15525, 127905, 1067925, 9004545, 76499525]
(r,k) = (-2,4) [1, 5, 33, 245, 1921, 15525, 127905, 1067925, 9004545, 76499525]
(r,k) = (-1,4) [1, 5, 33, 245, 1921, 15525, 127905, 1067925, 9004545, 76499525]
(r,k) = (1,4) [1, 5, 33, 245, 1921, 15525, 127905, 1067925, 9004545, 76499525]
(r,k) = (2,4) [1, 5, 33, 245, 1921, 15525, 127905, 1067925, 9004545, 76499525]
(r,k) = (3,4) [1, 5, 33, 245, 1921, 15525, 127905, 1067925, 9004545, 76499525]
(r,k) = (4,4) [1, 5, 33, 245, 1921, 15525, 127905, 1067925, 9004545, 76499525]
(r,k) = (5,4) [1, 5, 33, 245, 1921, 15525, 127905, 1067925, 9004545, 76499525]
(r,k) = (-5,5) [1, 6, 46, 396, 3606, 33876, 324556, 3151896, 30915046, 305543556]
(r,k) = (-4,5) [1, 6, 46, 396, 3606, 33876, 324556, 3151896, 30915046, 305543556]
(r,k) = (-3,5) [1, 6, 46, 396, 3606, 33876, 324556, 3151896, 30915046, 305543556]
(r,k) = (-2,5) [1, 6, 46, 396, 3606, 33876, 324556, 3151896, 30915046, 305543556]
(r,k) = (-1,5) [1, 6, 46, 396, 3606, 33876, 324556, 3151896, 30915046, 305543556]
(r,k) = (1,5) [1, 6, 46, 396, 3606, 33876, 324556, 3151896, 30915046, 305543556]
(r,k) = (2,5) [1, 6, 46, 396, 3606, 33876, 324556, 3151896, 30915046, 305543556]
(r,k) = (3,5) [1, 6, 46, 396, 3606, 33876, 324556, 3151896, 30915046, 305543556]
(r,k) = (4,5) [1, 6, 46, 396, 3606, 33876, 324556, 3151896, 30915046, 305543556]
(r,k) = (5,5) [1, 6, 46, 396, 3606, 33876, 324556, 3151896, 30915046, 305543556]
(r,k) = (-5,6) [1, 7, 61, 595, 6145, 65527, 712909, 7863667, 87615745, 983726695]
(r,k) = (-4,6) [1, 7, 61, 595, 6145, 65527, 712909, 7863667, 87615745, 983726695]
(r,k) = (-3,6) [1, 7, 61, 595, 6145, 65527, 712909, 7863667, 87615745, 983726695]
(r,k) = (-2,6) [1, 7, 61, 595, 6145, 65527, 712909, 7863667, 87615745, 983726695]
(r,k) = (-1,6) [1, 7, 61, 595, 6145, 65527, 712909, 7863667, 87615745, 983726695]
(r,k) = (1,6) [1, 7, 61, 595, 6145, 65527, 712909, 7863667, 87615745, 983726695]
(r,k) = (2,6) [1, 7, 61, 595, 6145, 65527, 712909, 7863667, 87615745, 983726695]
(r,k) = (3,6) [1, 7, 61, 595, 6145, 65527, 712909, 7863667, 87615745, 983726695]
(r,k) = (4,6) [1, 7, 61, 595, 6145, 65527, 712909, 7863667, 87615745, 983726695]
(r,k) = (5,6) [1, 7, 61, 595, 6145, 65527, 712909, 7863667, 87615745, 983726695]
(r,k) = (-5,7) [1, 8, 78, 848, 9766, 116208, 1411404, 17383584, 216294534, 2712176048]
(r,k) = (-4,7) [1, 8, 78, 848, 9766, 116208, 1411404, 17383584, 216294534, 2712176048]
(r,k) = (-3,7) [1, 8, 78, 848, 9766, 116208, 1411404, 17383584, 216294534, 2712176048]
(r,k) = (-2,7) [1, 8, 78, 848, 9766, 116208, 1411404, 17383584, 216294534, 2712176048]
(r,k) = (-1,7) [1, 8, 78, 848, 9766, 116208, 1411404, 17383584, 216294534, 2712176048]
(r,k) = (1,7) [1, 8, 78, 848, 9766, 116208, 1411404, 17383584, 216294534, 2712176048]
(r,k) = (2,7) [1, 8, 78, 848, 9766, 116208, 1411404, 17383584, 216294534, 2712176048]
(r,k) = (3,7) [1, 8, 78, 848, 9766, 116208, 1411404, 17383584, 216294534, 2712176048]
(r,k) = (4,7) [1, 8, 78, 848, 9766, 116208, 1411404, 17383584, 216294534, 2712176048]
(r,k) = (5,7) [1, 8, 78, 848, 9766, 116208, 1411404, 17383584, 216294534, 2712176048]
(r,k) = (-5,8) [1, 9, 97, 1161, 14721, 192969, 2582881, 35066313, 481003009, 6649718409]
(r,k) = (-4,8) [1, 9, 97, 1161, 14721, 192969, 2582881, 35066313, 481003009, 6649718409]
(r,k) = (-3,8) [1, 9, 97, 1161, 14721, 192969, 2582881, 35066313, 481003009, 6649718409]
(r,k) = (-2,8) [1, 9, 97, 1161, 14721, 192969, 2582881, 35066313, 481003009, 6649718409]
(r,k) = (-1,8) [1, 9, 97, 1161, 14721, 192969, 2582881, 35066313, 481003009, 6649718409]
(r,k) = (1,8) [1, 9, 97, 1161, 14721, 192969, 2582881, 35066313, 481003009, 6649718409]
(r,k) = (2,8) [1, 9, 97, 1161, 14721, 192969, 2582881, 35066313, 481003009, 6649718409]
(r,k) = (3,8) [1, 9, 97, 1161, 14721, 192969, 2582881, 35066313, 481003009, 6649718409]
(r,k) = (4,8) [1, 9, 97, 1161, 14721, 192969, 2582881, 35066313, 481003009, 6649718409]
(r,k) = (5,8) [1, 9, 97, 1161, 14721, 192969, 2582881, 35066313, 481003009, 6649718409]
(r,k) = (-5,9) [1, 10, 118, 1540, 21286, 304300, 4443580, 65830600, 985483270, 14869654300]
(r,k) = (-4,9) [1, 10, 118, 1540, 21286, 304300, 4443580, 65830600, 985483270, 14869654300]
(r,k) = (-3,9) [1, 10, 118, 1540, 21286, 304300, 4443580, 65830600, 985483270, 14869654300]
(r,k) = (-2,9) [1, 10, 118, 1540, 21286, 304300, 4443580, 65830600, 985483270, 14869654300]
(r,k) = (-1,9) [1, 10, 118, 1540, 21286, 304300, 4443580, 65830600, 985483270, 14869654300]
(r,k) = (1,9) [1, 10, 118, 1540, 21286, 304300, 4443580, 65830600, 985483270, 14869654300]
(r,k) = (2,9) [1, 10, 118, 1540, 21286, 304300, 4443580, 65830600, 985483270, 14869654300]
(r,k) = (3,9) [1, 10, 118, 1540, 21286, 304300, 4443580, 65830600, 985483270, 14869654300]
(r,k) = (4,9) [1, 10, 118, 1540, 21286, 304300, 4443580, 65830600, 985483270, 14869654300]
(r,k) = (5,9) [1, 10, 118, 1540, 21286, 304300, 4443580, 65830600, 985483270, 14869654300]
(r,k) = (-5,10) [1, 11, 141, 1991, 29761, 460251, 7272861, 116619591, 1889815041, 30869546411]
(r,k) = (-4,10) [1, 11, 141, 1991, 29761, 460251, 7272861, 116619591, 1889815041, 30869546411]
(r,k) = (-3,10) [1, 11, 141, 1991, 29761, 460251, 7272861, 116619591, 1889815041, 30869546411]
(r,k) = (-2,10) [1, 11, 141, 1991, 29761, 460251, 7272861, 116619591, 1889815041, 30869546411]
(r,k) = (-1,10) [1, 11, 141, 1991, 29761, 460251, 7272861, 116619591, 1889815041, 30869546411]
(r,k) = (1,10) [1, 11, 141, 1991, 29761, 460251, 7272861, 116619591, 1889815041, 30869546411]
(r,k) = (2,10) [1, 11, 141, 1991, 29761, 460251, 7272861, 116619591, 1889815041, 30869546411]
(r,k) = (3,10) [1, 11, 141, 1991, 29761, 460251, 7272861, 116619591, 1889815041, 30869546411]
(r,k) = (4,10) [1, 11, 141, 1991, 29761, 460251, 7272861, 116619591, 1889815041, 30869546411]
(r,k) = (5,10) [1, 11, 141, 1991, 29761, 460251, 7272861, 116619591, 1889815041, 30869546411]
(00:00) gp >