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%I #8 Jun 22 2017 11:47:20
%S 1,1,10,36,76,129,210,310,452,619,842,1096,1420,1781,2226,2714,3300,
%T 3935,4682,5484,6412,7401,8530,9726,11076,12499,14090,15760,17612,
%U 19549,21682,23906,26340,28871,31626,34484,37580,40785,44242,47814
%N Number of maximal cliques in the n X n queen graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximalClique.html">Maximal Clique</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/QueenGraph.html">Queen Graph</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -4, 1, 2, -1).
%F For n>3, a(n) = n*(73-3*(-1)^n+4*n*(2*n-3))/12-14.
%F For n>3, a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6).
%F G.f.: -((x^2*(-1+x-7*x^2-19*x^3+3*x^4+22*x^5-9*x^6-10*x^7+4*x^8))/((-1+x)^4*(1+x)^2)).
%t Table[Piecewise[{{1, n < 3}, {10, n == 3}}, n (73 - 3 (-1)^n + 4 n (2 n - 3))/12 - 14], {n, 20}]
%t Join[{1, 1}, LinearRecurrence[{2, 1, -4, 1, 2, -1}, {-28, -9, 10, 36, 76, 129}, {3, 20}]]
%t CoefficientList[Series[(1 - x + 7 x^2 + 19 x^3 - 3 x^4 - 22 x^5 + 9 x^6 + 10 x^7 - 4 x^8)/((-1 + x)^4 (1 + x)^2), {x, 0, 20}], x]
%K nonn
%O 1,3
%A _Eric W. Weisstein_, Jun 20 2017
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