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%I #9 Sep 21 2019 17:17:38
%S 4,20,80,320,1280,5120,20480,81920,327680,1310720,5242880,20971520,
%T 83886080,335544320,1342177280,5368709120,21474836480,85899345920,
%U 343597383680,1374389534720,5497558138880,21990232555520,87960930222080,351843720888320,1407374883553280
%N Number of 3-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) = 5*4^(n - 1) for n > 1.
%F a(n) = 4*a(n-1) for n > 2.
%F G.f. -4*x*(1 + x)/(-1 + 4 x).
%t Table[If[n == 1, 4, 5 4^(n - 1)], {n, 10}]
%t Join[{4}, LinearRecurrence[{4}, {20}, 30]]
%t CoefficientList[Series[-((4 (1 + x))/(-1 + 4 x)), {x, 0, 20}], x]
%t Join[{4},NestList[4#&,20,30]] (* _Harvey P. Dale_, Sep 21 2019 *)
%Y Cf. A003947, A269696.
%Y Cf. A292542 (4-cycles), A292543 (5-cycles), A292545 (6-cycles).
%K nonn
%O 1,1
%A _Eric W. Weisstein_, Sep 18 2017
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