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 A011797 #32 Mar 04 2025 07:55:02
%S A011797 0,0,0,0,0,0,0,1,4,12,30,66,132,245,429,715,1144,1768,2652,3876,5537,
%T A011797 7752,10659,14421,19228,25300,32890,42287,53820,67860,84825,105183,
%U A011797 129456,158224,192129,231880,278256
%N A011797 a(n) = floor(C(n,6)/7).
%C A011797 a(n-1) is the number of aperiodic necklaces (Lyndon words) with 7 black beads and n-7 white beads.
%H A011797 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 A011797 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 p. 19.
%H A011797 <a href="/index/Lu#Lyndon">Index entries for sequences related to Lyndon words</a>
%H A011797 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1,1,-6,15,-20,15,-6,1).
%F A011797 G.f.: (1+x^3)^2/((1-x)^4(1-x^2)^2(1-x^7))*x^7.
%F A011797 a(n) = floor(binomial(n+1,7)/(n+1)). [_Gary Detlefs_, Nov 23 2011]
%F A011797 G.f.: (x^6/7)*(1/(1-x)^7-1/(1- x^7)). - _Herbert Kociemba_, Oct 16 2016
%t A011797 CoefficientList[Series[x^6/7 (1/(1-x)^7-1/(1- x^7)),{x,0,40}],x]; (* _Herbert Kociemba_, Oct 16 2016 *)
%o A011797 (PARI) a(n) = binomial(n, 6)\7; \\ _Michel Marcus_, Oct 16 2016
%Y A011797 Cf. A000031, A001037, A051168. Same as A051172(n+1).
%Y A011797 First differences of A011853.
%Y A011797 A column of triangle A011847.
%K A011797 nonn,easy
%O A011797 0,9
%A A011797 _N. J. A. Sloane_, _David Broadhurst_