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A032167 Number of aperiodic necklaces of n beads of 12 colors. 3
12, 66, 572, 5148, 49764, 497354, 5118828, 53745120, 573308736, 6191711526, 67546215516, 743008120140, 8230246567620, 91708459194066, 1027134771622388, 11555266154065920, 130506535690613940 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..500

C. G. Bower, Transforms (2)

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

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

Index entries for sequences related to Lyndon words

FORMULA

"CHK" (necklace, identity, unlabeled) transform of 12, 0, 0, 0...

a(n) = Sum_{d|n} mu(d)*12^(n/d)/n.

MATHEMATICA

f[d_]:=MoebiusMu[d] 12^(n/d)/n; a[n_]:=Total[f/@Divisors[n]]; a[0]=1; Table[a[n], {n, 1, 30}] (* Vincenzo Librandi, Oct 14 2017 *)

CROSSREFS

Column 12 of A074650.

Sequence in context: A200190 A270251 A165107 * A039925 A091074 A212687

Adjacent sequences:  A032164 A032165 A032166 * A032168 A032169 A032170

KEYWORD

nonn

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified October 20 12:34 EDT 2018. Contains 316379 sequences. (Running on oeis4.)