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%I #13 Sep 26 2017 10:20:18
%S 0,218,876,3504,14016,56064,224256,897024,3588096,14352384,57409536,
%T 229638144,918552576,3674210304,14696841216,58787364864,235149459456,
%U 940597837824,3762391351296,15049565405184,60198261620736,240793046482944,963172185931776,3852688743727104
%N Number of 6-cycles in the n-Sierpinski tetrahedron graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</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_01">Index entries for linear recurrences with constant coefficients</a>, signature (4).
%F a(n) = 219*4^(n - 2) for n > 2.
%F a(n) = 4*a(n-1) for n > 2.
%F G.f.: -2*x^2*(109 + 2*x)/(-1 + 4*x).
%t Table[Piecewise[{{0, n == 1}, {218, n == 2}}, 219 4^(n - 2)], {n, 20}]
%t Join[{0, 218}, LinearRecurrence[{4}, {876}, 20]]
%t CoefficientList[Series[-2 x (109 + 2 x)/(-1 + 4 x), {x, 0, 20}], x]
%o (PARI) concat(0, Vec(-2*x^2*(109 + 2*x)/(-1 + 4*x) + O(x^50))) \\ _Michel Marcus_, Sep 19 2017
%Y Cf. A292540 (3-cycles), A292542 (4-cycles), A292543 (5-cycles).
%K nonn,easy
%O 1,2
%A _Eric W. Weisstein_, Sep 18 2017
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