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A008288","chain":null}}],"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:     1;\n  1:     3,      5;\n  2:     9,     39,      25;\n  3:    27,    189,     333,      125;\n  4:    81,    783,    2349,     2391,      625;\n  5:   243,   2997,   12825,    22725,    15657,      3125;\n  6:   729,  10935,   60993,   157167,   189729,     96939,     15625;\n  7:  2187,  38637,  266085,   906957,  1609281,   1438641,    578253,    78125;\n  8:  6561, 133407, 1094229,  4657095, 11038113,  14578407,  10198773,  3359631,   390625;\n  9: 19683, 452709, 4310577, 22042773, 65774025, 116760285, 120868281, 68818653, 19141137, 1953125;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (3*x-10*x^2)*P(n-2,x) + (3+7*x)*P(n-1,x) for n >= 2, with P(0,x) = 1, P(1,x) = 3 + 5*x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 3 + 5*x;\nP[n_, x_] := P[n, x] = Expand[(3*x - 10*x^2)*P[n - 2, x] + (3 + 7*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] = 1; v[2] = 3 + 5*x; for(n = 2, N, my(i = n + 1); v[i] = (3*x - 10*x^2)*v[i - 2] + (3 + 7*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-5733d79f45a14084","steps":["basis A008288","reverse"],"edges":["e-28556ceb40718bbf","e-9a4f8de1e11ee45a"],"text":"A013620 \u2192 basis A008288 \u2192 reverse"},"headline":"A013620 \u2192 basis A008288 \u2192 reverse","chain":null}