%I #6 Dec 28 2022 10:35:02
%S 4,9,30,61,160,301,718,1305,3000,5377,12190,21733,49024,87237,196446,
%T 349345,786232,1397881,3145486,5592141,12582624,22369309,50331310,
%U 89478121,201326200,357913521,805305918,1431655285,3221224960,5726622517,12884901310,22906491633
%N Number of (not necessarily maximal) cliques in the n X n white bishop 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/WhiteBishopGraph.html">White Bishop Graph</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2, 4, -10, 1, 8, -4).
%F a(n) = ((-1)^(n + 1) + 2^(n + 1)*(17 + (-1)^n) - 6*n*(n + 4) - 23)/12.
%F a(n) = 2*a(n-1) + 4*a(n-2) - 10*a(n-3) + a(n-4) + 8*a(n-5) - 4*a(n-6).
%F G.f.: x^2*(4 + x - 4*x^2 + 5*x^3 + 4*x^4 - 4*x^5)/((-1 + x)^3*(-1 - x + 4*x^2 + 4*x^3)).
%t Table[((-1)^(n + 1) + 2^(n + 1) (17 + (-1)^n) - 6 n (n + 4) - 23)/12, {n, 20}]
%t LinearRecurrence[{2, 4, -10, 1, 8, -4}, {4, 9, 30, 61, 160, 301}, 20]
%t Rest @ CoefficientList[Series[x (4 + x - 4 x^2 + 5 x^3 + 4 x^4 - 4 x^5)/((-1 + x)^3 (-1 - x + 4 x^2 + 4 x^3)), {x, 0, 20}], x]
%K nonn
%O 2,1
%A _Eric W. Weisstein_, Nov 29 2017