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A135552
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Triangular sequence from coefficients of general three deep polynomial recursion; here: c0=2; p(x, n) = (2 + c0 - x)*p(x, n - 1) + (-1 - c0 (2 - x))*p(x, n - 2) + c0*p(x, n - 3).
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0
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1, 4, -1, 11, -6, 1, 26, -22, 8, -1, 57, -64, 37, -10, 1, 120, -163, 130, -56, 12, -1, 247, -382, 386, -232, 79, -14, 1, 502, -848, 1024, -794, 378, -106, 16, -1, 1013, -1816, 2510, -2380, 1471, -576, 137, -18, 1, 2036, -3797, 5812, -6476, 4944, -2517, 834, -172, 20, -1, 4083, -7814, 12911, -16384, 14893, -9402
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums are: {1, 3, 6, 11, 21, 42, 85, 171, 342, 683, 1365}
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FORMULA
| c0=2; p(x, n) = (2 + c0 - x)*p(x, n - 1) + (-1 - c0 (2 - x))*p(x, n - 2) + c0*p(x, n - 3).
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EXAMPLE
| {1},
{4, -1},
{11, -6, 1},
{26, -22, 8, -1},
{57, -64, 37, -10, 1},
{120, -163, 130, -56, 12, -1},
{247, -382, 386, -232, 79, -14, 1},
{502, -848, 1024, -794, 378, -106, 16, -1},
{1013, -1816, 2510, -2380, 1471, -576, 137, -18, 1},
{2036, -3797, 5812, -6476, 4944, -2517, 834, -172, 20, -1},
{4083, -7814, 12911, -16384, 14893, -9402, 4048, -1160, 211, -22, 1}
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MATHEMATICA
| Clear[p, c0, x, n, a] (* c0 = 0 : A136674 : Triangular sequence made from matrices of the type(Cartan G_n types) : M(3) = {{2, -1, 0}, {-1, 2, -1}, {0, -3, 2}} with polynomial recursion : p(x, n) = (2 - x)*p(x, n - 1) - p(x, n - 2). *) (* c0 = 1 : 1 : A109954 : Riordan array (1/(1 + x)^3, x/(1 + x)^2). *) c0 = 2; p[x, -1] = 0; p[x, 0] = 1; p[x, 1] = 2 - x + c0; p[x_, n_] := p[x, n] = (2 + c0 - x)*p[x, n - 1] + (-1 - c0 (2 - x))*p[x, n - 2] + c0*p[x, n - 3]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
| Cf. A136674, A109954.
Sequence in context: A113897 A158753 A183884 * A181690 A109088 A060923
Adjacent sequences: A135549 A135550 A135551 * A135553 A135554 A135555
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KEYWORD
| uned,tabl,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 08 2008
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