A032166 Number of aperiodic necklaces of n beads of 11 colors.

11, 55, 440, 3630, 32208, 295020, 2783880, 26793030, 261994040, 2593726344, 25937424600, 261535549220, 2655593241840, 27124986721140, 278483211283552, 2871858103075830, 29732178147017280

Offset

1,1

Comments

Number of monic irreducible polynomials of degree n over GF(11). # Robert Israel, Jan 07 2015

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 11, 0, 0, 0...

a(n) = Sum_{d|n} mu(d)*11^(n/d)/n.

G.f.: Sum_{k>=1} mu(k)*log(1/(1 - 11*x^k))/k. - Ilya Gutkovskiy, May 19 2019

Maple

f:= (n, p) -> add(numtheory:-mobius(d)*p^(n/d), d=numtheory:-divisors(n))/n:
seq(f(n, 11), n=1..100); # Robert Israel, Jan 07 2015

Mathematica

f[d_]:=MoebiusMu[d] 11^(n/d)/n; a[n_]:=Total[f/@Divisors[n]]; a[0]=1; Table[a[n], {n, 1, 30}] (* Vincenzo Librandi, Oct 14 2017 *)

Prog

(PARI) a(n) = sumdiv(n, d, moebius(d)*11^(n/d))/n; \\ Michel Marcus, Jan 07 2015

Crossrefs

Column 11 of A074650.

Sequence in context: A246990 A156589 A165791 * A218000 A206528 A259193

Adjacent sequences: A032163 A032164 A032165 * A032167 A032168 A032169

Keyword

nonn

Author

Christian G. Bower

Status

approved