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%I #12 Dec 28 2022 10:34:48
%S 8,20,55,160,475,1420,4255,12760,38275,114820,344455,1033360,3100075,
%T 9300220,27900655,83701960,251105875,753317620,2259952855,6779858560,
%U 20339575675,61018727020,183056181055,549168543160,1647505629475,4942516888420,14827550665255
%N Number of (not necessarily maximal) cliques in the n-Sierpinski sieve graph.
%H G. C. Greubel, <a href="/A295933/b295933.txt">Table of n, a(n) for n = 1..1000</a>
%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/SierpinskiSieveGraph.html">Sierpinski Sieve Graph</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4, -3).
%F a(n) = 5*(3 + 7*3^(n - 1))/6 for n > 1.
%F a(n) = 4*a(n-1) - 3*a(n-2) for n > 1.
%F G.f.: x*(8 - 12*x - x^2)/(1 - 4*x + 3*x^2).
%F E.g.f.: (-80 - 6*x + 45*exp(x) + 35*exp(3*x))/18. - _G. C. Greubel_, May 21 2019
%t Table[If[n == 1, 8, 5*(3 + 7*3^(n-1))/6], {n, 30}]
%t Join[{8}, LinearRecurrence[{4, -3}, {20, 55}, 30]]
%t CoefficientList[Series[(8 -12x -x^2)/(1 -4x +3x^2), {x, 0, 30}], x]
%o (PARI) {a(n) = if(n==1, 8, 5*(1 +7*3^(n-2))/2)}; \\ _G. C. Greubel_, May 21 2019
%o (Magma) [n eq 1 select 8 else 5*(1 +7*3^(n-2))/2: n in [1..30]]; // _G. C. Greubel_, May 21 2019
%o (Sage) [8] + [5*(1 +7*3^(n-2))/2 for n in (2..30)] # _G. C. Greubel_, May 21 2019
%o (GAP) Concatenation([8], List([2..30], n-> 5*(1 +7*3^(n-2))/2 )) # _G. C. Greubel_, May 21 2019
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, Nov 29 2017
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