A114278 A triangle generated by a family of Sierpinski-triangle related polynomials.

1, 1, 1, 1, 3, 1, 1, 5, 3, 1, 1, 7, 7, 5, 1, 1, 9, 13, 15, 5, 1, 1, 11, 21, 35, 15, 7, 1, 1, 13, 31, 69, 35, 27, 7, 1, 1, 15, 43, 121, 71, 77, 29, 9, 1, 1, 17, 57, 195, 131, 183, 91, 45, 9, 1, 1, 19, 73, 295, 225, 385, 239, 165, 45, 11, 1

Offset

0,5

Comments

Inverse has row sums 0^n (conjecture). Row sums are A114279.

Links

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

Formula

Column k has g.f. x^k*sum{j=0..k, mod(C(k, j), 2)*x^j}/(1-x)^(k+1); Column k has g.f. x^k*sum{j=0..k, A001316(j)*A114280(k, j)*x^j/(1-x)^(j+1)}.

Example

Triangle begins
1;
1, 1;
1, 3, 1;
1, 5, 3, 1;
1, 7, 7, 5, 1;
1, 9,13,15, 5, 1;
1,11,21,35,15, 7, 1;

Crossrefs

Sequence in context: A181109 A152720 A131247 * A134836 A180955 A349182

Adjacent sequences: A114275 A114276 A114277 * A114279 A114280 A114281

Keyword

easy,nonn,tabl

Author

Paul Barry, Nov 20 2005

Status

approved