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%I #7 Dec 28 2022 10:37:54
%S 2,16,50,104,178,272,386,520,674,848,1042,1256,1490,1744,2018,2312,
%T 2626,2960,3314,3688,4082,4496,4930,5384,5858,6352,6866,7400,7954,
%U 8528,9122,9736,10370,11024,11698,12392,13106,13840,14594,15368,16162,16976,17810,18664,19538
%N Number of (not necessarily maximal) cliques in the n X n king graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Clique.html">Clique</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KingGraph.html">King Graph</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F a(n) = 2*(5*n^2 - 8*n + 4).
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F G.f.: -2*x*(1 + 5*x + 4*x^2)/(-1 + x)^3.
%t Table[2 (5 n^2 - 8 n + 4), {n, 20}]
%t LinearRecurrence[{3, -3, 1}, {2, 16, 50}, 20]
%t CoefficientList[Series[-2 (1 + 5 x + 4 x^2)/(-1 + x)^3, {x, 0, 20}], x]
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, Nov 29 2017
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