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A045629 Number of 2n-bead black-white complementable necklaces with n black beads. 6
1, 1, 2, 3, 7, 15, 44, 128, 415, 1367, 4654, 16080, 56450, 200170, 716728, 2585850, 9393119, 34319667, 126047906, 465076160, 1723097066, 6407856892, 23910271224, 89493903438, 335912741682, 1264106399934, 4768448177636, 18027218147818 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200

Index entries for sequences related to necklaces

FORMULA

a(n) = (1/2n) * Sum_{d|n} (phi(n/d)*C(2d-1, d-1) + phi(2n/d)*2^(d-1)). - Christian G. Bower

a(n) ~ 4^(n-1) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Oct 08 2017

MATHEMATICA

a[n_] := If[n == 0, 1, (1/(2*n))*DivisorSum[n, EulerPhi[n/#1]*Binomial[2*#1 - 1, #1 - 1] + EulerPhi[2*(n/#1)]*2^(#1 - 1)&]];

Table[a[n], {n, 0, 27}] (* Jean-Fran├žois Alcover, Oct 08 2017, translated from PARI *)

PROG

(PARI) a(n) = if(n==0, 1, (1/(2*n)) * sumdiv(n, d, eulerphi(n/d)*binomial(2*d-1, d-1) + eulerphi(2*n/d)*2^(d-1))); \\ Andrew Howroyd, Sep 27 2017

CROSSREFS

Cf. A006840.

Sequence in context: A289470 A213385 A161746 * A034731 A216435 A110888

Adjacent sequences:  A045626 A045627 A045628 * A045630 A045631 A045632

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified December 11 18:46 EST 2019. Contains 329925 sequences. (Running on oeis4.)