A137696 Triangular sequence of coefficients from a polynomial recursion: p(x,n)=p(x,Floor[(n-1)/2])-x^2*p(x,n-3)+x.

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

Offset

1,8

Comments

Row sums are: {1, 1, 2, 1, 1, 1, 2, 1, 1, 0, 1, ...}

Links

Table of n, a(n) for n=1..51.

Formula

p(x,n)=p(x,Floor[(n-1)/2])-x^2*p(x,n-3)+x; out_n,m=Coefficient(p(x,n)).

Example

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

Mathematica

Clear[p, x]; p[x, -1] = 0; p[x, 0] = 1; p[x, 1] = x; p[x, 2] = x^2 + x; p[x_, n_] := p[x, n] = p[x, Floor[(n - 1)/2]] - x^2*p[x, n - 3] + x; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[p[x, n], x]], {n, 0, 10}];

Crossrefs

Sequence in context: A033768 A033786 A366768 * A275731 A143614 A071412

Adjacent sequences: A137693 A137694 A137695 * A137697 A137698 A137699

Keyword

tabl,sign

Author

Roger L. Bagula, Apr 27 2008

Status

approved