

A032165


Number of aperiodic necklaces of n beads of 10 colors.


3



10, 45, 330, 2475, 19998, 166485, 1428570, 12498750, 111111000, 999989991, 9090909090, 83333249175, 769230769230, 7142856428565, 66666666659934, 624999993750000, 5882352941176470, 55555555499944500
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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
F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc. [Cached copy, with permission, pdf format only]


FORMULA

"CHK" (necklace, identity, unlabeled) transform of 10, 0, 0, 0...
a(n) = Sum_{dn} mu(d)*10^(n/d)/n.


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



