

A045629


Number of 2nbead blackwhite 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
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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_{dn} (phi(n/d)*C(2d1, d1) + phi(2n/d)*2^(d1)).  Christian G. Bower
a(n) ~ 4^(n1) / (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}] (* JeanFrançois 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*d1, d1) + eulerphi(2*n/d)*2^(d1))); \\ 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



