A032229 Number of ways to partition n elements into pie slices of different odd sizes allowing the pie to be turned over.

1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 7, 5, 7, 6, 11, 8, 14, 9, 21, 23, 24, 25, 34, 39, 40, 53, 53, 80, 62, 106, 138, 145, 150, 184, 232, 247, 307, 310, 452, 398, 593, 485, 864, 969, 1068, 1093, 1465, 1613, 1855, 2145, 2438, 3074, 3014

Offset

0,9

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

C. G. Bower, Transforms (2)

Formula

"DGK" (bracelet, element, unlabeled) transform of 1, 0, 1, 0... (odds).

Prog

(PARI) seq(n)={Vec(1 + sum(k=1, sqrtint(n), my(r=k^2); if(k>2, (k-1)!, 2) * x^r / prod(j=1, k, 1 - x^(2*j) + O(x*x^(n-r))))/2)} \\ Andrew Howroyd, Sep 20 2018

Crossrefs

Sequence in context: A132322 A018118 A029084 * A024366 A218123 A288157

Adjacent sequences: A032226 A032227 A032228 * A032230 A032231 A032232

Keyword

nonn

Author

Christian G. Bower

Extensions

a(0)=1 prepended by Andrew Howroyd, Sep 20 2018

Status

approved