A045632 Number of 2n-bead black-white complementable necklaces with n black beads and fundamental period 2n.

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

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}] (* Jean-François 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