A115124 Number of imprimitive (periodic) 2n-bead black-white reversible complementable necklaces with n black beads.
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
Offset: 0
Programs
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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 *)
Extensions
More terms from Jean-François Alcover, Aug 28 2019
Comments