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%I #8 Dec 30 2023 14:30:51
%S 0,0,6,16,50,96,196,320,540,800,1210,1680,2366,3136,4200,5376,6936,
%T 8640,10830,13200,16170,19360,23276,27456,32500,37856,44226,50960,
%U 58870,67200,76880,87040,98736,110976,124950,139536,156066,173280,192660
%N Number of 4-cycles in the n X n white bishop graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WhiteBishopGraph.html">White Bishop Graph</a>.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).
%F a(n) = (n - 1)^2*(2*n^2 - 4*n - 3 + 3*(-1)^n)/24.
%F a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8).
%F G.f.: -2*x^4*(3+2*x+3*x^2)/((-1+x)^5*(1+x)^3).
%t Table[(n - 1)^2 (2 n^2 - 4 n - 3 + 3 (-1)^n)/24, {n, 2, 20}]
%t LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {0, 0, 6, 16, 50, 96, 196, 320}, 20]
%t CoefficientList[Series[-2 x^2 (3 + 2 x + 3 x^2)/((-1 + x)^5 (1 + x)^3), {x, 0, 20}], x]
%K nonn,easy
%O 2,3
%A _Eric W. Weisstein_, Dec 07 2023
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