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%I #10 Aug 05 2017 11:56:15
%S 0,0,0,0,4,13,98,415,1151,2471,4385,6893,9995,13691,17981,22865,28343,
%T 34415,41081,48341,56195,64643,73685,83321,93551,104375,115793,127805,
%U 140411,153611,167405,181793,196775,212351,228521,245285,262643,280595
%N Number of 6-cycles in the n-triangular honeycomb obtuse knight graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F For n >= 9, a(n) = 16001 - 4323*n + 297*n^2.
%F For n >= 12, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3).
%F G.f.: x^5*(-4 - x - 71*x^2 - 156*x^3 - 187*x^4 - 165*x^5 - 10*x^6)/(-1 +
%F x)^3.
%t Table[Piecewise[{{0, n <= 4}, {4, n == 5}, {13, n == 6}, {98, n == 7}, {415, n == 8}, {16001 - 4323 n + 297 n^2, n > 8}}, 0], {n, 20}]
%t Join[{0, 0, 0, 0, 4, 13, 98, 415}, LinearRecurrence[{3, -3, 1}, {1151, 2471, 4385}, 12]]
%t CoefficientList[Series[(x^4 (-4 - x - 71 x^2 - 156 x^3 - 187 x^4 - 165 x^5 - 10 x^6))/(-1 + x)^3, {x, 0, 20}], x]
%Y Cf. A001105 (3-cycles in the triangular honeycomb obtuse knight graph), A194715 (4-cycles), A290391 (5-cycles).
%K nonn,easy
%O 1,5
%A _Eric W. Weisstein_, Jul 29 2017
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