A137406 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);.

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

Offset

1,3

Comments

A002530 is the row sums:

{1, -1, -3, 4, 11, -15, -41, 56, 153, -209, -571}

Links

Table of n, a(n) for n=1..66.

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);

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}

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]

Crossrefs

Cf. A002530.

Sequence in context: A324469 A329688 A217920 * A181293 A262876 A263045

Adjacent sequences: A137403 A137404 A137405 * A137407 A137408 A137409

Keyword

tabl,uned,sign

Author

Roger L. Bagula, Apr 14 2008

Status

approved