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

Author

Christian G. Bower

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500
• C. G. Bower, Transforms (2)

Crossrefs

Cf. A000005, A027750, A032190 (CIK, pie not to be turned over).

Programs

Maple

A032278_list := proc(n)
    local ele ;
    ele := [0,seq(1,i=1..30)] ;
    DIK(ele) ; # defined in A032287
end proc:
A032278_list(50) ; # R. J. Mathar, Feb 14 2025

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

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