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Number of (not necessarily maximal) cliques in the n-sun graph.
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%I #6 Dec 28 2022 10:38:23

%S 6,12,20,32,52,88,156,288,548,1064,2092,4144,8244,16440,32828,65600,

%T 131140,262216,524364,1048656,2097236,4194392,8388700,16777312,

%U 33554532,67108968,134217836,268435568,536871028,1073741944,2147483772,4294967424,8589934724

%N Number of (not necessarily maximal) cliques in the n-sun graph.

%C Extended to a(1)-a(2) using the formula.

%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/SunGraph.html">Sun Graph</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4, -5, 2).

%F a(n) = 2^n + 4*n.

%F a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).

%F G.f.: -2*x*(3 - 6*x + x^2)/((-1 + x)^2*(-1 + 2*x)).

%t Table[2^n + 4 n, {n, 20}]

%t LinearRecurrence[{4, -5, 2}, {6, 12, 20}, 20]

%t CoefficientList[Series[-2 (3 - 6 x + x^2)/((-1 + x)^2 (-1 + 2 x)), {x, 0, 20}], x]

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Nov 29 2017