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A137406
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Triangular sequence from coefficients of a switched even -odd polynomial recursion: Even:p(x,n)=2*x*p(x, n - 1) - p(x, n - 2); Odd:p(x,n)=(1 - 2*x)*p(x, n - 1) - p(x, n - 2);.
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0
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1, 1, -2, -1, 2, -4, -2, 6, -8, 8, 1, -6, 16, -16, 16, 3, -14, 36, -56, 48, -32, -1, 12, -44, 88, -128, 96, -64, -4, 28, -104, 232, -352, 384, -256, 128, 1, -20, 100, -296, 592, -800, 832, -512, 256, 5, -50, 244, -728, 1536, -2368, 2688, -2304, 1280, -512, -1, 30, -200, 784, -2048, 3872, -5568, 5888, -4864, 2560, -1024
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| A002530 is the row sums:
{1, -1, -3, 4, 11, -15, -41, 56, 153, -209, -571}
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FORMULA
| p(x,-1)=0;p(x,0)=1;p(x,1]=1-28x; Even:p(x,n)=2*x*p(x, n - 1) - p(x, n - 2); Odd:p(x,n)=(1 - 2*x)*p(x, n - 1) - p(x, n - 2);
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EXAMPLE
| {1},
{1, -2},
{-1, 2, -4},
{-2, 6, -8, 8},
{1, -6, 16, -16, 16},
{3, -14, 36, -56, 48, -32},
{-1, 12, -44, 88, -128, 96, -64},
{-4, 28, -104, 232, -352, 384, -256, 128},
{1, -20, 100, -296, 592, -800, 832, -512, 256},
{5, -50, 244, -728, 1536, -2368, 2688, -2304, 1280, -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] = 1 - 2*x; p[x_, n_] := p[x, n] = If[Mod[n, 2] == 0, 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. A002530.
Sequence in context: A120253 A060547 A079878 * A181293 A201912 A201908
Adjacent sequences: A137403 A137404 A137405 * A137407 A137408 A137409
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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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