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%I #7 Jul 14 2017 13:30:45
%S 0,0,0,0,920,17760,122640,537040,1794240,4994640,12178320,26840880,
%T 54620280,104184080,188348160,325459680,541078720,869994720,
%U 1358615520,2067768480,3075954840,4483100160,6414845360,9027424560,12513177600,17106746800,23092009200
%N Number of 6-cycles in the n-tetrahedral graph.
%C Extended to a(1)-a(5) using the formula.
%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/TetrahedralGraph.html">Tetrahedral Graph</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).
%F a(n) = 5*binomial(n, 5)*(454 - 409*n + 66*n^2 + n^3).
%F a(n) = 9*a(n-1)-36*a(n-2)+84*a(n-3)-126*a(n-4)+126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9).
%F G.f.: (40*x^5*(-23 - 237*x + 102*x^2 + 116*x^3))/(-1 + x)^9.
%t Table[5 Binomial[n, 5] (454 - 409 n + 66 n^2 + n^3), {n, 20}]
%t LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {0, 0, 0, 0, 920, 17760, 122640, 537040, 1794240}, 20]
%t CoefficientList[Series[(40 x^4 (-23 - 237 x + 102 x^2 + 116 x^3))/(-1 + x)^9, {x, 0, 20}], x]
%Y Cf. A027789 (3-cycles), A289792 (4-cycles), A289793 (5-cycles).
%K nonn,easy
%O 1,5
%A _Eric W. Weisstein_, Jul 12 2017
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