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A045633 Number of 2n-bead black-white reversible complementable necklaces with n black beads and fundamental period 2n. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified July 5 19:02 EDT 2020. Contains 335473 sequences. (Running on oeis4.)