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

0,4

Links

Table of n, a(n) for n=0..27.

Index entries for sequences related to bracelets

Formula

Moebius transform of A006840 (Christian Bower).

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 *)

Crossrefs

Sequence in context: A071359 A160999 A014329 * A090826 A132441 A000840

Adjacent sequences: A045630 A045631 A045632 * A045634 A045635 A045636

Keyword

nonn

Author

David W. Wilson

Status

approved