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v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}},{"oeis_id":"A125662","target":"triangle","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":true,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:    1;\n  1:    3,     1;\n  2:    8,     6,     1;\n  3:   21,    25,     9,     1;\n  4:   55,    90,    51,    12,     1;\n  5:  144,   300,   234,    86,    15,    1;\n  6:  377,   954,   951,   480,   130,   18,    1;\n  7:  987,  2939,  3573,  2305,   855,  183,   21,   1;\n  8: 2584,  8850, 12707, 10008,  4740, 1386,  245,  24,  1;\n  9: 6765, 26195, 43398, 40426, 23373, 8715, 2100, 316, 27, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (3+x)*P(n-1,x) - P(n-2,x) for n >= 2, with P(0,x) = 1, P(1,x) = 3 + x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 3 + x;\nP[n_, x_] := P[n, x] = Expand[(3 + x)*P[n - 1, x] - P[n - 2, x]];\nTable[PadRight[CoefficientList[P[n, x], x], n + 1], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 3 + x; for(n = 2, N, my(i = n + 1); v[i] = (3 + x)*v[i - 1] - v[i - 2]); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n + 1 - #c)); 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":true}}],"derivation":{"root":"n-f287bed89e07609f","steps":[],"edges":[],"text":"A125662"},"headline":"A125662: A convolution triangle of numbers based on A001906 (even-indexed Fibonacci numbers).","chain":null}