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%I #12 Aug 28 2019 08:16:15
%S 1,1,1,2,5,14,40,127,408,1364,4638,16079,56401,200169,716599,2585833,
%T 9392704,34319666,126046498,465076159,1723092407,6407856762,
%U 23910255143,89493903437,335912684824,1264106399919,4768447977465,18027218146451
%N Number of 2n-bead black-white complementable necklaces with n black beads and fundamental period 2n.
%H <a href="/index/Lu#Lyndon">Index entries for sequences related to Lyndon words</a>
%F Moebius transform of A045629 (Christian Bower).
%t A045629[n_] := If[n == 0, 1, (1/(2n)) DivisorSum[n, EulerPhi[n/#] Binomial[ 2#-1, #-1] + EulerPhi[2(n/#)] 2^(#-1)&]];
%t a[n_] := If[n == 0, 1, Sum[MoebiusMu[n/d] A045629[d], {d, Divisors[n]}]];
%t Table[a[n], {n, 0, 27}] (* _Jean-François Alcover_, Aug 28 2019 *)
%K nonn
%O 0,4
%A _David W. Wilson_
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