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A032189 Number of ways to partition n elements into pie slices each with an odd number of elements. 0
1, 1, 2, 2, 3, 4, 5, 7, 10, 14, 19, 30, 41, 63, 94, 142, 211, 328, 493, 765, 1170, 1810, 2787, 4340, 6713, 10461, 16274, 25414, 39651, 62074, 97109, 152287, 238838, 375166, 589527, 927554, 1459961, 2300347, 3626242, 5721044, 9030451, 14264308, 22542397, 35646311, 56393862, 89264834, 141358275 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..47.

C. G. Bower, Transforms (2)

P. Flajolet and M. Soria, The Cycle Construction In SIAM J. Discr. Math., vol. 4 (1), 1991, pp. 58-60.

Index entries for sequences related to necklaces

FORMULA

a(n) = A000358(n)-(1+(-1)^n)/2.

"CIK" (necklace, indistinct, unlabeled) transform of 1, 0, 1, 0...(odds)

G.f. sum(k>=1, phi(k)/k * log( 1/(1-B(x^k)) ) ) where B(x)=x/(1-x^2).  [Joerg Arndt, Aug 06 2012]

PROG

(PARI)

N=66;  x='x+O('x^N);

B(x)=x/(1-x^2);

A=sum(k=1, N, eulerphi(k)/k*log(1/(1-B(x^k))));

Vec(A)

/* Joerg Arndt, Aug 06 2012 */

CROSSREFS

Cf. A008965

Sequence in context: A097600 A173674 A018128 * A186425 A034395 A032232

Adjacent sequences:  A032186 A032187 A032188 * A032190 A032191 A032192

KEYWORD

nonn

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified July 25 12:01 EDT 2014. Contains 244910 sequences.