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Number of (not necessarily maximal) cliques in the n X n knight graph.
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%I #6 Dec 28 2022 10:38:08

%S 2,5,18,41,74,117,170,233,306,389,482,585,698,821,954,1097,1250,1413,

%T 1586,1769,1962,2165,2378,2601,2834,3077,3330,3593,3866,4149,4442,

%U 4745,5058,5381,5714,6057,6410,6773,7146,7529,7922,8325,8738,9161,9594,10037,10490,10953

%N Number of (not necessarily maximal) cliques in the n X n knight 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/KnightGraph.html">Knight 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) = 5*n^2 - 12*n + 9.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

%F G.f.: x*(-2 + x - 9 x^2)/(-1 + x)^3.

%t Table[5 n^2 - 12 n + 9, {n, 20}]

%t LinearRecurrence[{3, -3, 1}, {2, 5, 18}, 20]

%t CoefficientList[Series[(-2 + x - 9 x^2)/(-1 + x)^3, {x, 0, 20}], x]

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Nov 29 2017