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 A032166 Number of aperiodic necklaces of n beads of 11 colors. 3
 11, 55, 440, 3630, 32208, 295020, 2783880, 26793030, 261994040, 2593726344, 25937424600, 261535549220, 2655593241840, 27124986721140, 278483211283552, 2871858103075830, 29732178147017280 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 1 23:26 EST 2023. Contains 367503 sequences. (Running on oeis4.)