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%I #8 Apr 12 2018 09:49:21
%S 0,5,50,265,996,2985,7610,17185,35320,67341,120770,205865,336220,
%T 529425,807786,1199105,1737520,2464405,3429330,4691081,6318740,
%U 8392825,11006490,14266785,18295976,23232925,29234530,36477225,45158540,55498721,67742410,82160385,99051360
%N Number of 6-cycles in the (n+5)-path complement 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/PathComplementGraph.html">Path Complement Graph</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F G.f.: x*(-5 - 15*x - 20*x^2 - 16*x^3 - 3*x^4 - x^5)/(-1 + x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
%F a(n) = n*(4 + 22*n + 17*n^2 + 13*n^3 + 3*n^4 + n^5)/12.
%t Table[n (4 + 22 n + 17 n^2 + 13 n^3 + 3 n^4 + n^5)/12, {n, 0, 20}]
%t LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {5, 50, 265, 996, 2985, 7610, 17185}, {0, 20}]
%t CoefficientList[Series[x (-5 - 15 x - 20 x^2 - 16 x^3 - 3 x^4 - x^5)/(-1 + x)^7, {x, 0, 20}], x]
%o (PARI) a(n) = n*(4+22*n+17*n^2+13*n^3+3*n^4+n^5)/12; \\ _Altug Alkan_, Apr 12 2018
%Y Cf. A000292 (3-cycles of \bar P_{n+4}), A002817 (4-cycles of \bar P_{n+4}), A060446 (5-cycles of \bar P_{n+3}).
%K nonn,easy
%O 0,2
%A _Eric W. Weisstein_, Apr 11 2018
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