cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A032296 Number of aperiodic bracelets (turnover necklaces) with n beads of 5 colors.

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%I A032296 #30 Apr 30 2019 14:53:28
%S A032296 5,10,30,105,372,1460,5890,25275,110050,492744,2227270,10195070,
%T A032296 46989180,218096780,1017447736,4768944375,22440372240,105966686200,
%U A032296 501938733550,2384200190580,11353290083380
%N A032296 Number of aperiodic bracelets (turnover necklaces) with n beads of 5 colors.
%H A032296 C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%H A032296 F. Ruskey, <a href="http://combos.org/necklace">Necklaces, Lyndon words, De Bruijn sequences, etc.</a>
%H A032296 F. Ruskey, <a href="/A000011/a000011.pdf">Necklaces, Lyndon words, De Bruijn sequences, etc.</a> [Cached copy, with permission, pdf format only]
%H A032296 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A032296 <a href="/index/Br#bracelets">Index entries for sequences related to bracelets</a>
%F A032296 MOEBIUS transform of A032276.
%F A032296 From _Herbert Kociemba_, Nov 28 2016: (Start)
%F A032296 More generally, gf(k) is the g.f. for the number of bracelets with primitive period n and beads of k colors.
%F A032296 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 A032296 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 A032296 Column 5 of A276550.
%K A032296 nonn
%O A032296 1,1
%A A032296 _Christian G. Bower_