A045633 Number of 2n-bead black-white reversible complementable necklaces with n black beads and fundamental period 2n.

1, 1, 1, 2, 5, 12, 31, 84, 250, 762, 2504, 8358, 28928, 101339, 361184, 1297864, 4707712, 17179434, 63068079, 232615770, 861723271, 3204236692, 11955827898, 44748176652, 167959114814, 632058070297, 2384234976235, 9013628450510

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Links

• Index entries for sequences related to bracelets

Programs

Mathematica

b[n_] := (1/(2n)) DivisorSum[n, EulerPhi[n/#] Binomial[2# - 1, # - 1] + EulerPhi[2(n/#)] 2^(# - 1) &];
A006840[n_] := If[n == 0, 1, (b[n] + 2^(n - 2) + Binomial[n - Mod[n, 2], Quotient[n, 2]]/2)/2];
a[n_] := If[n == 0, 1, Sum[MoebiusMu[n/d] A006840[d], {d, Divisors[n]}]];
Array[a, 30, 0] (* Jean-François Alcover, Aug 28 2019 *)

Formula

Moebius transform of A006840 (Christian Bower).