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A032295 Number of aperiodic bracelets (turn over necklaces) with n beads of 4 colors. 1
4, 6, 16, 45, 132, 404, 1296, 4380, 15064, 53622, 192696, 703895, 2589300, 9606744, 35824088, 134297280, 505421340, 1909194056, 7234153416, 27489073899, 104717489748, 399827555604, 1529763696816 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..23.

C. G. Bower, Transforms (2)

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

N. J. A. Sloane, Transforms

Index entries for sequences related to bracelets

FORMULA

MOEBIUS transform of A032275.

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, 4], {x, 0, mx}], x] (* Herbert Kociemba, Nov 28 2016 *)

CROSSREFS

Column 4 of A276550.

Sequence in context: A165799 A231998 A056421 * A072279 A038236 A223269

Adjacent sequences:  A032292 A032293 A032294 * A032296 A032297 A032298

KEYWORD

nonn

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified February 25 16:14 EST 2018. Contains 299653 sequences. (Running on oeis4.)