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row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}},{"oeis_id":"A038222","target":"reversed_triangle","first_row":0,"oeis_offset":0,"reversed":true,"trim_zeros":"none","regular_triangle":true,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:     1;\n  1:     3,      4;\n  2:     9,     24,      16;\n  3:    27,    108,     144,      64;\n  4:    81,    432,     864,     768,     256;\n  5:   243,   1620,    4320,    5760,    3840,     1024;\n  6:   729,   5832,   19440,   34560,   34560,    18432,    4096;\n  7:  2187,  20412,   81648,  181440,  241920,   193536,   86016,   16384;\n  8:  6561,  69984,  326592,  870912, 1451520,  1548288, 1032192,  393216,   65536;\n  9: 19683, 236196, 1259712, 3919104, 7838208, 10450944, 9289728, 5308416, 1769472, 262144;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where P(n,x) = (4+3*x)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(4 + 3*x)*P[n - 1, x]];\nTable[Reverse[PadRight[CoefficientList[P[n, x], x], n + 1]], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = (4 + 3*x)*v[i - 1]); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n + 1 - #c)); c = Vecrev(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":true,"trim_zeros":"none","regular_triangle":true}},{"oeis_id":"A038233","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:      4,       3;\n  2:     16,      24,       9;\n  3:     64,     144,     108,      27;\n  4:    256,     768,     864,     432,       81;\n  5:   1024,    3840,    5760,    4320,     1620,     243;\n  6:   4096,   18432,   34560,   34560,    19440,    5832,     729;\n  7:  16384,   86016,  193536,  241920,   181440,   81648,   20412,    2187;\n  8:  65536,  393216, 1032192, 1548288,  1451520,  870912,  326592,   69984,   6561;\n  9: 262144, 1769472, 5308416, 9289728, 10450944, 7838208, 3919104, 1259712, 236196, 19683;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (4+3*x)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(4 + 3*x)*P[n - 1, 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; for(n = 1, N, my(i = n + 1); v[i] = (4 + 3*x)*v[i - 1]); 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-6a5af5e1168bb679","steps":["basis A007318"],"edges":["e-5bade392cbb9f615"],"text":"A013610 \u2192 basis A007318"},"headline":"A013610 \u2192 basis A007318","chain":null}