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%I #10 Dec 30 2023 13:16:35
%S 0,0,1,38,276,1270,4745,15936,50608,156116,474585,1432450,4309076,
%T 12942618,38847601,116567660,349733760,1049238856,3147761873,
%U 9443339646,28330082740,84990322910,254971055481,764913266488,2294739914096,6884219872860,20652659766505
%N Number of 6-cycles in the n-Dorogovtsev-Goltsev-Mendes graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Dorogovtsev-Goltsev-MendesGraph.html">Dorogovtsev-Goltsev-Mendes Graph</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (7, -18, 22, -13, 3).
%F a(n) = (65*3^n - 84*n - 6*n^2 - 40*n^3 - 65)/8.
%F a(n) = 7*a(n-1) - 18*a(n-2) + 22*a(n-3) - 13*a(n-4) + 3*a(n-5).
%F G.f.: -x^2*(1+31*x+28*x^2)/((-1+x)^4*(-1+3*x)).
%t Table[(65 3^n - 84 n - 6 n^2 - 40 n^3 - 65)/8, {n, 0, 20}]
%t LinearRecurrence[{7, -18, 22, -13, 3}, {0, 0, 1, 38, 276}, 20]
%Y Cf. A003462(n) (3-cycles), A290764(n-1) (4-cycles), A367967(n) (5-cycles).
%K nonn,easy
%O 0,4
%A _Eric W. Weisstein_, Dec 06 2023
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