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0]"}]}],"used_by":[],"used_by_total":0,"links":[],"oeis":[],"bfiles":[],"oeis_texts":[{"oeis_id":"","target":"node","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:         89,         324,          288;\n  1:        610,        3312,         5904,          3456;\n  2:       4181,       30180,        80784,         95040,         41472;\n  3:      28657,      258120,       921744,       1631232,       1430784,         497664;\n  4:     196418,     2120544,      9468864,      22384512,      29548800,       20653056,        5971968;\n  5:    1346269,    16942704,     90806832,     268686720,     474024960,      498659328,      289640448,       71663616;\n  6:    9227465,   132633612,    829491408,    2948104512,    6512866560,     9158261760,     8005423104,     3977330688,      859963392;\n  7:   63245986,  1022222160,   7307236368,   30321941760,   80493295104,   141763571712,   165647462400,   123834728448,    53747712000,    10319560704;\n  8:  433494437,  7781873340,  62587829088,  296992324224,  920803500288,  1949106281472,  2852689674240,  2850635317248,  1861390761984,   717209468928,  123834728448;\n  9: 2971215073, 58652824464, 524190047328, 2799678276864, 9929039097600, 24551622402048, 43192455634944, 54062888583168, 47183611428864, 27346835865600, 9473356726272, 1486016741376;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = -P(n-2,x) + (7+12*x)*P(n-1,x) for n >= 2, with P(0,x) = 89 + 324*x + 288*x^2, P(1,x) = 610 + 3312*x + 5904*x^2 + 3456*x^3.","mathematica":"P[0, x_] := 89 + 324*x + 288*x^2;\nP[1, x_] := 610 + 3312*x + 5904*x^2 + 3456*x^3;\nP[n_, x_] := P[n, x] = Expand[-P[n - 2, x] + (7 + 12*x)*P[n - 1, x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 89 + 324*x + 288*x^2; v[2] = 610 + 3312*x + 5904*x^2 + 3456*x^3; for(n = 2, N, my(i = n + 1); v[i] = -v[i - 2] + (7 + 12*x)*v[i - 1]); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-dfab35176bd08e72","steps":["basis A013611","basis A013610"],"edges":["e-b12bbff1e34cdc3a","e-76296f2a906d8153"],"text":"A207606 \u2192 basis A013611 \u2192 basis A013610"},"headline":"A207606 \u2192 basis A013611 \u2192 basis A013610","chain":null}