A066315 -id:A066315 - cp's OEIS frontend

A066316 Number of identity (asymmetric) bracelets (or necklaces) with n red and blue beads such that the beads switch colors when bracelet is turned over.

1, 5, 24, 91, 340, 1224, 4365, 15521, 55311, 197964, 712243, 2577105, 9375360, 34284971, 125977464, 464938189, 1722817415, 6407307543, 23909159417, 89491715105, 335908316844, 1264097675775, 4768430557020, 18027183349395

Offset: 4

Christian G. Bower, Dec 13 2001

nonn

Index entries for sequences related to bracelets

a(n)=A022553(n)-A066315(n)

A115123 Number of imprimitive (periodic) bracelets (or necklaces) with n red and blue beads such that the beads switch colors when bracelet is turned over.

Original entry on oeis.org

0, 1, 1, 2, 1, 5, 1, 9, 4, 22, 1, 63, 1, 156, 24, 469, 1, 1532, 1, 4889, 158, 16546, 1, 57844, 21, 202061, 1480, 720533, 1, 2598406, 1, 9408469, 16548, 34350508, 175, 126167112, 1, 465200334, 202063, 1723346534, 1, 6409076632, 1, 23911272097, 2594970, 89495909410, 1

Offset: 1

Valery A. Liskovets, Jan 17 2006

a(p)=1 for prime p.

A006080[n_] := Sum[EulerPhi[(n - 1)/k] (Binomial[2k, k]/(2(n - 1))), {k, Divisors[n - 1]}]/2 + 2^(n - 3); A006080[1] = 1;
A066315[n_] := Sum[MoebiusMu[n/d] A006080[d + 1], {d, Divisors[n]}];
a[n_] := A006080[n + 1] - A066315[n];
Array[a, 60] (* Jean-François Alcover, Aug 28 2019 *)

a(n)=A006080(n+1) - A066315(n).

More terms from Jean-François Alcover, Aug 28 2019

cp's OEIS Frontend

A066316 Number of identity (asymmetric) bracelets (or necklaces) with n red and blue beads such that the beads switch colors when bracelet is turned over.

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A115123 Number of imprimitive (periodic) bracelets (or necklaces) with n red and blue beads such that the beads switch colors when bracelet is turned over.

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