A032165 Number of aperiodic necklaces of n beads of 10 colors.

10, 45, 330, 2475, 19998, 166485, 1428570, 12498750, 111111000, 999989991, 9090909090, 83333249175, 769230769230, 7142856428565, 66666666659934, 624999993750000, 5882352941176470, 55555555499944500

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.

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

Index entries for sequences related to Lyndon words

Formula

"CHK" (necklace, identity, unlabeled) transform of 10, 0, 0, 0...

a(n) = Sum_{d|n} mu(d)*10^(n/d)/n.

G.f.: Sum_{k>=1} mu(k)*log(1/(1 - 10*x^k))/k. - Ilya Gutkovskiy, May 19 2019

Mathematica

f[d_]:=MoebiusMu[d] 10^(n/d)/n; a[n_]:=Total[f/@Divisors[n]]; a[0]=1; Table[a[n], {n, 1, 20}] (* Vincenzo Librandi, Oct 14 2017 *)

Prog

(PARI) a(n) = sumdiv(n, d, moebius(d)*10^(n/d))/n; \\ Andrew Howroyd, Oct 13 2017

Crossrefs

Column 10 of A074650.

Sequence in context: A278641 A219709 A061772 * A124174 A264414 A188699

Adjacent sequences: A032162 A032163 A032164 * A032166 A032167 A032168

Keyword

nonn

Author

Christian G. Bower

Status

approved