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

Author

David W. Wilson

Keywords

• nonn

Links

• Index entries for sequences related to Lyndon words

Programs

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 *)

Formula

Moebius transform of A045629 (Christian Bower).