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A137408
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Triangular sequence from coefficients of a switched even -odd polynomial recursion: odd:p(x,n)=2*x*p(x, n - 1) - p(x, n - 2); even:p(x,n)=(1 - 2*x)*p(x, n - 1) - p(x, n - 2);.
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0
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1, 0, 2, -1, 2, -4, 0, -4, 4, -8, 1, -6, 16, -16, 16, 0, 6, -16, 40, -32, 32, -1, 12, -44, 88, -128, 96, -64, 0, -8, 40, -128, 208, -288, 192, -128, 1, -20, 100, -296, 592, -800, 832, -512, 256, 0, 10, -80, 328, -800, 1472, -1792, 1792, -1024, 512, -1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| A048788 gives the row sums: {1, 2, -3, -8, 11, 30, -41, -112, 153, 418, -571}
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FORMULA
| p(x,-1)=0;p(x,0)=1;p(x,1]=2*x; odd:p(x,n)=2*x*p(x, n - 1) - p(x, n - 2); even:p(x,n)=(1 - 2*x)*p(x, n - 1) - p(x, n - 2);
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EXAMPLE
| {1},
{0, 2},
{-1, 2, -4},
{0, -4, 4, -8},
{1, -6, 16, -16,16},
{0, 6, -16, 40, -32, 32},
{-1, 12, -44, 88, -128, 96, -64},
{0, -8, 40, -128, 208, -288, 192, -128},
{1, -20, 100, -296, 592, -800, 832, -512, 256},
{0,10, -80, 328, -800,1472, -1792, 1792, -1024, 512},
{-1, 30, -200, 784, -2048, 3872, -5568, 5888, -4864, 2560, -1024}
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MATHEMATICA
| Clear[p, x, a] p[x, -1] = 0; p[x, 0] = 1; p[x, 1] = 2*x; p[x_, n_] := p[x, n] = If[Mod[n, 2] == 1, 2*x*p[x, n - 1] - p[x, n - 2], (1 - 2*x)*p[x, n - 1] - p[x, n - 2]]; 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. A048788.
Sequence in context: A061678 A206425 A131022 * A007461 A181302 A143446
Adjacent sequences: A137405 A137406 A137407 * A137409 A137410 A137411
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KEYWORD
| tabl,uned,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 14 2008
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