

A045632


Number of 2nbead blackwhite complementable necklaces with n black beads and fundamental period 2n.


1



1, 1, 1, 2, 5, 14, 40, 127, 408, 1364, 4638, 16079, 56401, 200169, 716599, 2585833, 9392704, 34319666, 126046498, 465076159, 1723092407, 6407856762, 23910255143, 89493903437, 335912684824, 1264106399919, 4768447977465, 18027218146451
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OFFSET

0,4


LINKS

Table of n, a(n) for n=0..27.
Index entries for sequences related to Lyndon words


FORMULA

Moebius transform of A045629 (Christian Bower).


MATHEMATICA

A045629[n_] := If[n == 0, 1, (1/(2n)) DivisorSum[n, EulerPhi[n/#] Binomial[ 2#1, #1] + EulerPhi[2(n/#)] 2^(#1)&]];
a[n_] := If[n == 0, 1, Sum[MoebiusMu[n/d] A045629[d], {d, Divisors[n]}]];
Table[a[n], {n, 0, 27}] (* JeanFrançois Alcover, Aug 28 2019 *)


CROSSREFS

Sequence in context: A301871 A076866 A151417 * A148321 A007463 A159308
Adjacent sequences: A045629 A045630 A045631 * A045633 A045634 A045635


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



