

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, 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
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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((1x^(2*d))/(1x^dx^(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



