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 A006565 M4942 #41 Jul 08 2025 16:49:30 %S A006565 0,1,14,130,700,2635,7826,19684,43800,88725,166870,295526,498004, %T A006565 804895,1255450,1899080,2796976,4023849,5669790,7842250,10668140, %U A006565 14296051,18898594,24674860,31853000,40692925,51489126,64573614 %N A006565 Number of ways to color vertices of a hexagon using <= n colors, allowing only rotations. %D A006565 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A006565 Victor Meally, <a href="/A006556/a006556.pdf">Letter to N. J. A. Sloane</a>, no date. %H A006565 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009. %H A006565 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992 %H A006565 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1). %F A006565 n*(n+1)*(n^2+n+1)*(n^2-2*n+2)/6. %p A006565 A006565 := n-> (n^6+n^3+2*n^2+2*n)/6. %p A006565 A006565:=-(1+7*z+53*z**2+49*z**3+10*z**4)/(z-1)**7; [Conjectured by _Simon Plouffe_ in his 1992 dissertation.] %Y A006565 Cf. A027670, A075195. %K A006565 nonn %O A006565 0,3 %A A006565 _N. J. A. Sloane_