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.
%I A011796 #30 Mar 04 2025 07:55:06
%S A011796 1,3,9,20,42,75,132,212,333,497,728,1026,1428,1932,2583,3384,4389,
%T A011796 5598,7084,8844,10962,13442,16380,19776,23751,28301,33561,39536,46376,
%U A011796 54081,62832,72624,83655,95931,109668,124866,141778,160398
%N A011796 Number of irreducible alternating Euler sums of depth 6 and weight 6+2n.
%C A011796 a(n-6) is the number of aperiodic necklaces (Lyndon words) with 6 black beads and n-6 white beads.
%D A011796 J. M. Borwein, D. H. Bailey and R. Girgensohn, Experimentation in Mathematics, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See p. 147.
%H A011796 David J. Broadhurst, <a href="http://arXiv.org/abs/hep-th/9604128">On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory</a>, arXiv:hep-th/9604128, 1996.
%H A011796 David Broadhurst and Xavier Roulleau, <a href="https://arxiv.org/abs/2502.19523">Number of partitions of modular integers</a>, arXiv:2502.19523 [math.NT], 2025. See pp. 3, 11, 19.
%H A011796 <a href="/index/Lu#Lyndon">Index entries for sequences related to Lyndon words</a>
%H A011796 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-3,-1,1,4,-3,-3,4,1,-1,-3,1,2,-1).
%F A011796 G.f.: x*(1+x+2*x^2+2*x^3+3*x^4+2*x^6+x^7)/((1-x)^2*(1-x^2)^2*(1-x^3)*(1-x^6)).
%F A011796 G.f.: (1/(1-x)^6-1/(1-x^2)^3-1/(1-x^3)^2+1/(1-x^6))/6. - _Herbert Kociemba_, Oct 23 2016
%F A011796 a(n) = T(n,6), array T as in A051168.
%p A011796 a:= n-> (Matrix([[42, 20, 9, 3, 1, 0$7, -1, -4, -9]]). Matrix(15, (i,j)-> if (i=j-1) then 1 elif j=1 then [2, 1, -3, -1, 1, 4, -3, -3, 4, 1, -1, -3, 1, 2, -1][i] else 0 fi)^(n-5))[1,1]: seq(a(n), n=1..50); # _Alois P. Heinz_, Aug 04 2008
%t A011796 a[n_] := Sum[Binomial[(n+6)/d, 6/d]*MoebiusMu[d],{d, Divisors[GCD[6, n+6]]}]/(n+6); Array[a, 40] (* _Jean-François Alcover_, Feb 02 2015 *)
%Y A011796 Cf. A000031, A001037, A051168.
%K A011796 nonn,easy
%O A011796 1,2
%A A011796 _N. J. A. Sloane_, _David Broadhurst_