|
%I #4 Sep 18 2017 21:53:16
%S 16,59,227,899,3587,14339,57347,229379,917507,3670019,14680067,
%T 58720259,234881027,939524099,3758096387,15032385539,60129542147,
%U 240518168579,962072674307,3848290697219,15393162788867,61572651155459,246290604621827,985162418487299
%N Number of cliques in the n-Sierpinski tetrahedron 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/SierpinskiTetrahedronGraph.html">Sierpinski Tetrahedron Graph</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5, -4).
%F a(n) = 7*4^n/2 + 3 for n > 1.
%F a(n) = 5*a(n-1) - 4*a(n-2) for n > 1.
%F G.f.: x*(16 - 21*x - 4*x^2)/(1 - 5*x + 4*x^2).
%t Table[Piecewise[{{16, n == 1}}, 7 4^n/2 + 3], {n, 20}]
%t Join[{16}, LinearRecurrence[{5, -4}, {59, 227}, 20]]
%t CoefficientList[Series[(16 - 21 x - 4 x^2)/(1 - 5 x + 4 x^2), {x, 0, 20}], x]
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, Sep 18 2017
|
