A123230 Triangle read by rows: T(n,k) is the coefficient of x^k in the polynomial p(n,x) defined by p(0,x)=1, p(1,x)=1+x, p(n,x)=xp(n-1,x)+(-1)^(n+1)p(n-2,x) for n>=2.

1, 1, 1, -1, 1, 1, 1, 0, 1, 1, 1, 0, -1, 1, 1, 1, 1, 1, 0, 1, 1, -1, 1, 2, 0, -1, 1, 1, 1, 0, 2, 2, 1, 0, 1, 1, 1, 0, -2, 2, 3, 0, -1, 1, 1, 1, 1, 2, 0, 3, 3, 1, 0, 1, 1, -1, 1, 3, 0, -3, 3, 4, 0, -1, 1, 1

Offset

0,24

Links

Table of n, a(n) for n=0..65.

Example

{1},
{1, 1},
{-1, 1, 1},
{1, 0, 1, 1},
{1, 0, -1, 1, 1},
{1, 1, 1, 0, 1, 1},
{-1, 1, 2, 0, -1, 1, 1},
{1, 0, 2, 2, 1, 0, 1, 1},
{1, 0, -2, 2, 3, 0, -1, 1,1},
{1, 1, 2, 0, 3, 3, 1, 0, 1, 1},
{-1, 1, 3, 0, -3, 3, 4, 0, -1, 1, 1}

Maple

P[0]:=1: P[1]:=1+x: for n from 2 to 14 do P[n]:=sort(expand(x*P[n-1]+(-1)^(n+1)*P[n-2])) od: for n from 0 to 14 do seq(coeff(P[n], x, k), k=0..n) od; # yields sequence in triangular form

Mathematica

p[0, x] = 1; p[1, x] = x + 1; p[k_, x_] := p[k, x] = x*p[k - 1, x] + (-1)^(n + 1)p[k - 2, x]; w = Table[CoefficientList[p[n, x], x], {n, 0, 10}]; Flatten[w]

Crossrefs

Sequence in context: A112202 A126205 A025913 * A078821 A125184 A236575

Adjacent sequences: A123227 A123228 A123229 * A123231 A123232 A123233

Keyword

sign,tabl

Author

Roger L. Bagula, Oct 06 2006

Extensions

Edited by N. J. A. Sloane, Oct 29 2006

Status

approved