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 A288918 #23 Feb 16 2025 08:33:48
%S A288918 0,3,29,79,153,251,373,519,689,883,1101,1343,1609,1899,2213,2551,2913,
%T A288918 3299,3709,4143,4601,5083,5589,6119,6673,7251,7853,8479,9129,9803,
%U A288918 10501,11223,11969,12739,13533,14351,15193,16059,16949,17863
%N A288918 Number of 4-cycles in the n X n king graph.
%H A288918 Colin Barker, <a href="/A288918/b288918.txt">Table of n, a(n) for n = 1..1000</a>
%H A288918 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A288918 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KingGraph.html">King Graph</a>
%H A288918 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A288918 a(n) = 12*n^2 - 34*n + 23 for n > 1. - _Andrew Howroyd_, Jun 19 2017
%F A288918 From _Colin Barker_, Mar 11 2019: (Start)
%F A288918 G.f.: x^2*(3 + 20*x + x^2) / (1 - x)^3.
%F A288918 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 4. (End)
%F A288918 E.g.f.: exp(x)*(23 - 22*x + 12*x^2) - 23 - x. - _Stefano Spezia_, Aug 14 2022
%t A288918 Table[If[n == 1, 0, 23 - 34 n + 12 n^2], {n, 20}]
%t A288918 Join[{0}, LinearRecurrence[{3, -3, 1}, {1, 3, 29}, {2, 20}]]
%t A288918 CoefficientList[Series[(-3 x - 20 x^2 - x^3)/(-1 + x)^3, {x, 0, 20}],x]
%o A288918 (PARI) a(n)=if(n, 12*n^2-10*n+1, 0) \\ _Charles R Greathouse IV_, Jun 19 2017
%o A288918 (PARI) concat(0, Vec(x^2*(3 + 20*x + x^2) / (1 - x)^3 + O(x^40))) \\ _Colin Barker_, Mar 11 2019
%Y A288918 Cf. A016742 (3-cycles), A288919 (5-cycles), A288920 (6-cycles).
%K A288918 nonn,easy
%O A288918 1,2
%A A288918 _Eric W. Weisstein_, Jun 19 2017