A146565 A double offset polynomial as a triangle of coefficients: p(x,n)=(x + 1)^n + If[n >= 2, x^2*(x + 1)^(n - 1), x^(n + 1)] + If[n >= 4, x^2*(x + 1)^(n - 3), 0].

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 4, 3, 1, 1, 4, 8, 8, 4, 1, 1, 5, 12, 16, 12, 5, 1, 1, 6, 17, 28, 28, 17, 6, 1, 1, 7, 23, 45, 56, 45, 23, 7, 1, 1, 8, 30, 68, 101, 101, 68, 30, 8, 1, 1, 9, 38, 98, 169, 202, 169, 98, 38, 9, 1, 1, 10, 47, 136, 267, 371, 371, 267, 136, 47, 10, 1

Offset

0,8

Comments

Row sums are {1, 2, 3, 6, 12, 26, 52, 104, 208, 416, 832, 1664, ...}, A259098.

Links

Table of n, a(n) for n=0..77.

Formula

p(x,n)=(x + 1)^n + If[n >= 2, x^2*(x + 1)^(n - 1), x^(n + 1)] + If[n >= 4, x^2*(x + 1)^(n - 3), 0]; t(n,m)=Coefficients(p(x,n)).

Example

Triangle begins:
{1},
{1, 1},
{1, 1, 1},
{1, 2, 2, 1},
{1, 3, 4, 3, 1},
{1, 4, 8, 8, 4, 1},
{1, 5, 12, 16, 12, 5, 1},
{1, 6, 17, 28, 28, 17, 6, 1},
{1, 7, 23, 45, 56, 45, 23, 7, 1},
{1, 8, 30, 68, 101, 101, 68, 30, 8, 1},
{1, 9, 38, 98, 169, 202, 169, 98, 38, 9, 1},
{1, 10, 47, 136, 267, 371, 371, 267, 136, 47, 10, 1},
...

Mathematica

p[x_, n_] = (x + 1)^n + If[n >= 2, x^2*(x + 1)^(n - 1), x^(n + 1)] + If[n >= 4, x^2*(x + 1)^(n - 3), 0]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]

Crossrefs

Cf. A072405, A259098.

Sequence in context: A047089 A122218 A072405 * A115594 A086623 A248736

Adjacent sequences: A146562 A146563 A146564 * A146566 A146567 A146568

Keyword

nonn,tabl

Author

Roger L. Bagula, Nov 01 2008

Extensions

Partially edited by N. J. A. Sloane, Jun 22 2015

Status

approved