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 A291910 #12 Feb 16 2025 08:33:51
%S A291910 0,0,9,576,6900,44100,196245,686784,2023056,5232600,12224025,26310240,
%T A291910 52936884,100663836,182452725,317318400,532407360,865571184,
%U A291910 1368508041,2110550400,3183182100,4705372980,6829824309,9750223296,13709610000,19009965000,26023131225
%N A291910 Number of 4-cycles in the n X n rook complement graph.
%H A291910 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A291910 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>
%H A291910 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).
%F A291910 a(n) = (n-2)*(n-1)^2*n^2*(-4 + 5*n - 4*n^2 + n^3)/8.
%F A291910 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9).
%F A291910 G.f.: -((3 x^3 (3 + 165 x + 680 x^2 + 660 x^3 + 165 x^4 + 7 x^5))/(-1 + x)^9).
%t A291910 Table[(-2 + n) (-1 + n)^2 n^2 (-4 + 5 n - 4 n^2 + n^3)/8, {n, 20}]
%t A291910 LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {0, 0, 9, 576, 6900, 44100, 196245, 686784, 2023056}, 30]
%t A291910 CoefficientList[Series[-((3 x^2 (3 + 165 x + 680 x^2 + 660 x^3 + 165 x^4 + 7 x^5))/(-1 + x)^9), {x, 0, 20}], x]
%Y A291910 Cf. A179058 (3-cycles), A291911 (5-cycles), A291912 (6-cycles).
%K A291910 nonn
%O A291910 1,3
%A A291910 _Eric W. Weisstein_, Sep 05 2017