A032278 Number of ways to partition n elements into pie slices each with at least 2 elements allowing the pie to be turned over.

0, 1, 1, 2, 2, 4, 4, 7, 8, 13, 15, 25, 30, 48, 63, 98, 132, 208, 290, 454, 656, 1021, 1509, 2358, 3544, 5535, 8441, 13200, 20318, 31835, 49352, 77435, 120710, 189673, 296853, 467159, 733362, 1155646, 1818593, 2869377, 4524080

Offset

1,4

Comments

A134681(n) = A055642(a(n)). - Reinhard Zumkeller, Nov 06 2007

Links

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

C. G. Bower, Transforms (2)

Formula

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

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

Prog

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

Crossrefs

Cf. A000005, A027750.

Sequence in context: A035554 A183567 A222710 * A222738 A005308 A151532

Adjacent sequences: A032275 A032276 A032277 * A032279 A032280 A032281

Keyword

nonn

Author

Christian G. Bower

Status

approved