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%I #6 Dec 28 2022 10:36:58
%S 17,153,1289,10521,84809,680409,5449097,43610265,348934601,2791634265,
%T 22333546505,178669789209,1429362565193,11434913276121,91479344472713,
%U 731834870572953,5854679308957385,46837435504780377,374699487137606921,2997595906398947097,23980767279085851977
%N Number of (not necessarily maximal) cliques in the n-Sierpinski carpet 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/SierpinskiCarpetGraph.html">Sierpinski Carpet Graph</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12, -35, 24).
%F a(n) = (13*8^n - 8*3^n + 5)/5.
%F a(n) = 12*a(n-1) - 35*a(n-2) + 24*a(n-3).
%F G.f.: x*(-17 + 51*x - 48*x^2)/(-1 + 12*x - 35*x^2 + 24*x^3).
%t Table[(13 8^n - 8 3^n + 5)/5, {n, 10}]
%t LinearRecurrence[{12, -35, 24}, {17, 153, 1289}, 20]
%t CoefficientList[Series[(-17 + 51 x - 48 x^2)/(-1 + 12 x - 35 x^2 + 24 x^3), {x, 0, 20}], x]
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, Nov 29 2017