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A032168 Number of aperiodic necklaces of n beads of 2 colors, 10 of them black. 5
1, 5, 22, 70, 200, 497, 1144, 2424, 4862, 9225, 16796, 29372, 49742, 81686, 130750, 204248, 312455, 468611, 690690, 1001400, 1430715, 2015871, 2804880, 3856528, 5245125, 7060508, 9414328, 12440056, 16301164 (list; graph; refs; listen; history; text; internal format)
OFFSET

11,2

LINKS

Table of n, a(n) for n=11..39.

C. G. Bower, Transforms (2)

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

Index entries for sequences related to Lyndon words

FORMULA

"CHK[ 10 ]" (necklace, identity, unlabeled, 10 parts) transform of 1, 1, 1, 1...

G.f.:  x^10 (1/(1-x)^10-1/(1-x^2)^5-1/(1-x^5)^2+1/(1-x^10))/10. - Herbert Kociemba, Oct 23 2016

MATHEMATICA

(* The g.f. given above is the special case k=10 for *)

gf[x_, k_]:=x^k/k Plus@@(MoebiusMu[#](1-x^#)^(-(k/#))&/@Divisors[k])

(* which gives the  g.f. for the number of aperiodic necklaces of n beads of 2 colors, k of them black. *) (* Herbert Kociemba, Oct 23 2016 *)

CROSSREFS

Sequence in context: A222632 A273336 A273768 * A246211 A000345 A011846

Adjacent sequences:  A032165 A032166 A032167 * A032169 A032170 A032171

KEYWORD

nonn

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified February 23 00:33 EST 2018. Contains 299473 sequences. (Running on oeis4.)