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A115124 Number of imprimitive (periodic) 2n-bead black-white reversible complementable necklaces with n black beads. 0
0, 0, 1, 1, 2, 1, 4, 1, 7, 3, 14, 1, 40, 1, 86, 15, 257, 1, 797, 1, 2523, 87, 8360, 1, 29218, 13, 101341, 765, 361275, 1, 1300415, 1, 4707969, 8361, 17179436, 97, 63097809, 1, 232615772, 101342, 861726044, 1, 3204597995, 1, 11955836263, 1298641, 44748176654, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(p)=1 for prime p.

LINKS

Table of n, a(n) for n=0..47.

FORMULA

a(n)=A006840(n) - A045633(n).

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];

A045633[n_] := If[n==0, 1, Sum[MoebiusMu[n/d] A006840[d], {d, Divisors[n]}] ];

a[n_] := A006840[n] - A045633[n];

Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Aug 28 2019 *)

CROSSREFS

Sequence in context: A088522 A252751 A199744 * A115122 A097360 A325348

Adjacent sequences:  A115121 A115122 A115123 * A115125 A115126 A115127

KEYWORD

easy,nonn

AUTHOR

Valery A. Liskovets, Jan 17 2006

EXTENSIONS

More terms from Jean-François Alcover, Aug 28 2019

STATUS

approved

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Last modified September 18 07:26 EDT 2020. Contains 337166 sequences. (Running on oeis4.)