A032277 Number of ways to partition n elements into pie slices each with an odd number of elements allowing the pie to be turned over.

1, 1, 2, 2, 3, 4, 5, 7, 9, 13, 16, 25, 31, 48, 64, 98, 133, 208, 291, 454, 657, 1021, 1510, 2358, 3545, 5535, 8442, 13200, 20319, 31835, 49353, 77435, 120711, 189673, 296854, 467159, 733363, 1155646, 1818594, 2869377, 4524081

Offset

1,3

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

C. G. Bower, Transforms (2)

Formula

"DIK" (bracelet, indistinct, unlabeled) transform of 1, 0, 1, 0, ... (odds)

G.f.: (x*(1 + x - x^4)/((1 - x)*(1 + x)*(1 - x^2 - x^4)) + Sum_{d>0} phi(d)*log((1 - x^(2*d))/(1 - x^d - x^(2*d)))/d)/2. - Andrew Howroyd, Jun 20 2018

Prog

(PARI) seq(n)={Vec(x*(1 + x - x^4)/((1 - x)*(1 + x)*(1 - x^2 - x^4)) + sum(d=1, n, eulerphi(d)/d*log((1-x^(2*d))/(1-x^d-x^(2*d)) + O(x*x^n))))/2} \\ Andrew Howroyd, Jun 20 2018

Crossrefs

Sequence in context: A072493 A064324 A173090 * A205579 A089047 A133498

Adjacent sequences: A032274 A032275 A032276 * A032278 A032279 A032280

Keyword

nonn

Author

Christian G. Bower

Status

approved