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%I #30 Apr 30 2019 14:53:28
%S 5,10,30,105,372,1460,5890,25275,110050,492744,2227270,10195070,
%T 46989180,218096780,1017447736,4768944375,22440372240,105966686200,
%U 501938733550,2384200190580,11353290083380
%N Number of aperiodic bracelets (turnover necklaces) with n beads of 5 colors.
%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%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 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Br#bracelets">Index entries for sequences related to bracelets</a>
%F MOEBIUS transform of A032276.
%F From _Herbert Kociemba_, Nov 28 2016: (Start)
%F More generally, gf(k) is the g.f. for the number of bracelets with primitive period n and beads of k colors.
%F gf(k): Sum_{n>=1} mu(n)*( -log(1-k*x^n)/n + Sum_{i=0..2} binomial(k,i)x^(n*i)/(1-k*x^(2*n)) )/2. (End)
%t mx=40;gf[x_,k_]:=Sum[ MoebiusMu[n]*(-Log[1-k*x^n]/n+Sum[Binomial[k,i]x^(n i),{i,0,2}]/( 1-k x^(2n)))/2,{n,mx}]; CoefficientList[Series[gf[x,5],{x,0,mx}],x] (* _Herbert Kociemba_, Nov 28 2016 *)
%Y Column 5 of A276550.
%K nonn
%O 1,1
%A _Christian G. Bower_
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