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A032166 Number of aperiodic necklaces of n beads of 11 colors. 3


%S 11,55,440,3630,32208,295020,2783880,26793030,261994040,2593726344,

%T 25937424600,261535549220,2655593241840,27124986721140,

%U 278483211283552,2871858103075830,29732178147017280

%N Number of aperiodic necklaces of n beads of 11 colors.

%C Number of monic irreducible polynomials of degree n over GF(11). # _Robert Israel_, Jan 07 2015

%H Vincenzo Librandi, <a href="/A032166/b032166.txt">Table of n, a(n) for n = 1..500</a>

%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>

%H Y. Puri and T. Ward, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/WARD/short.html">Arithmetic and growth of periodic orbits</a>, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

%H F. Ruskey, <a href="http://combos.org/necklace">Necklaces, Lyndon words, De Bruijn sequences, etc.</a>

%H F. Ruskey, <a href="/A000011/a000011.pdf">Necklaces, Lyndon words, De Bruijn sequences, etc.</a> [Cached copy, with permission, pdf format only]

%H <a href="/index/Lu#Lyndon">Index entries for sequences related to Lyndon words</a>

%F "CHK" (necklace, identity, unlabeled) transform of 11, 0, 0, 0...

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

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

%p f:= (n,p) -> add(numtheory:-mobius(d)*p^(n/d),d=numtheory:-divisors(n))/n:

%p seq(f(n,11), n=1..100); # _Robert Israel_, Jan 07 2015

%t 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 *)

%o (PARI) a(n) = sumdiv(n, d, moebius(d)*11^(n/d))/n; \\ _Michel Marcus_, Jan 07 2015

%Y Column 11 of A074650.

%K nonn

%O 1,1

%A _Christian G. Bower_

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Last modified August 5 06:37 EDT 2021. Contains 346458 sequences. (Running on oeis4.)