A032296 Number of aperiodic bracelets (turnover necklaces) with n beads of 5 colors.

5, 10, 30, 105, 372, 1460, 5890, 25275, 110050, 492744, 2227270, 10195070, 46989180, 218096780, 1017447736, 4768944375, 22440372240, 105966686200, 501938733550, 2384200190580, 11353290083380

Offset

1,1

Links

Table of n, a(n) for n=1..21.

C. G. Bower, Transforms (2)

F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.

F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc. [Cached copy, with permission, pdf format only]

N. J. A. Sloane, Transforms

Index entries for sequences related to bracelets

Formula

MOEBIUS transform of A032276.

From Herbert Kociemba, Nov 28 2016: (Start)

More generally, gf(k) is the g.f. for the number of bracelets with primitive period n and beads of k colors.

gf(k): Sum_{n>=1} mu(n)*( -log(1-k*x^n)/n + Sum_{i=0..2} binomial(k,i)x^(n*i)/(1-k*x^(2*n)) )/2. (End)

Mathematica

mx=40; gf[x_, k_]:=Sum[ MoebiusMu[n]*(-Log[1-k*x^n]/n+Sum[Binomial[k, i]x^(n i), {i, 0, 2}]/( 1-k x^(2n)))/2, {n, mx}]; CoefficientList[Series[gf[x, 5], {x, 0, mx}], x] (* Herbert Kociemba, Nov 28 2016 *)

Crossrefs

Column 5 of A276550.

Sequence in context: A358728 A189315 A056422 * A052648 A020995 A174467

Adjacent sequences: A032293 A032294 A032295 * A032297 A032298 A032299

Keyword

nonn

Author

Christian G. Bower

Status

approved