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 A288961 #19 Feb 16 2025 08:33:48
%S A288961 0,0,6,32,100,240,490,896,1512,2400,3630,5280,7436,10192,13650,17920,
%T A288961 23120,29376,36822,45600,55860,67760,81466,97152,115000,135200,157950,
%U A288961 183456,211932,243600,278690,317440,360096,406912,458150,514080,574980,641136,712842,790400
%N A288961 Number of 3-cycles in the n X n rook graph.
%H A288961 Andrew Howroyd, <a href="/A288961/b288961.txt">Table of n, a(n) for n = 1..1000</a>
%H A288961 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A288961 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookGraph.html">Rook Graph</a>
%H A288961 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A288961 a(n) = 2*n*binomial(n,3).
%F A288961 a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5).
%F A288961 G.f.: (-2*x^3*(3+x))/(-1+x)^5.
%t A288961 Table[n^2 (n - 1) (n - 2)/3, {n, 20}]
%t A288961 Table[2 n Binomial[n, 3], {n, 20}]
%t A288961 LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 6, 32, 100}, 20]
%t A288961 CoefficientList[Series[-((2 x^2 (3 + x))/(-1 + x)^5), {x, 0, 20}], x]
%o A288961 (PARI) a(n) = {2*n*binomial(n,3)} \\ _Andrew Howroyd_, Apr 26 2020
%Y A288961 Cf. A288962 (4-cycles), A288963 (5-cycles), A288960 (6-cycles).
%Y A288961 Main diagonal of A360855.
%K A288961 nonn,easy
%O A288961 1,3
%A A288961 _Eric W. Weisstein_, Jun 20 2017
%E A288961 Terms a(31) and beyond from _Andrew Howroyd_, Apr 26 2020