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%I #15 Aug 22 2017 20:53:09
%S 6,15,50,210,882,4220,20640,107100,563730,3036411,16514100,90778485,
%T 502474350,2799199380,15673672238,88162569180,497847963690,
%U 2821127257950,16035812864940,91404065292036
%N Number of primitive (period n) bracelets using a maximum of six different colored beads.
%C Turning over will not create a new bracelet.
%D M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
%F sum mu(d)*A056341(n/d) where d|n.
%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,6],{x,0,mx}],x] (* _Herbert Kociemba_, Nov 28 2016 *)
%Y Column 6 of A276550.
%Y Cf. A032164.
%K nonn
%O 1,1
%A _Marks R. Nester_
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