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%I A032295 #23 Apr 30 2019 08:24:52
%S A032295 4,6,16,45,132,404,1296,4380,15064,53622,192696,703895,2589300,
%T A032295 9606744,35824088,134297280,505421340,1909194056,7234153416,
%U A032295 27489073899,104717489748,399827555604,1529763696816
%N A032295 Number of aperiodic bracelets (turn over necklaces) with n beads of 4 colors.
%H A032295 C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%H A032295 F. Ruskey, <a href="http://combos.org/necklace">Necklaces, Lyndon words, De Bruijn sequences, etc.</a>
%H A032295 F. Ruskey, <a href="/A000011/a000011.pdf">Necklaces, Lyndon words, De Bruijn sequences, etc.</a> [Cached copy, with permission, pdf format only]
%H A032295 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A032295 <a href="/index/Br#bracelets">Index entries for sequences related to bracelets</a>
%F A032295 MOEBIUS transform of A032275.
%F A032295 From _Herbert Kociemba_, Nov 28 2016: (Start)
%F A032295 More generally, gf(k) is the g.f. for the number of bracelets with primitive period n and beads of k colors.
%F A032295 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 A032295 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,4],{x,0,mx}],x] (* _Herbert Kociemba_, Nov 28 2016 *)
%Y A032295 Column 4 of A276550.
%K A032295 nonn
%O A032295 1,1
%A A032295 _Christian G. Bower_

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