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Number of 5-cycles in the n-triangular honeycomb obtuse knight graph.
3

%I #9 Aug 05 2017 11:55:09

%S 0,0,0,0,0,0,30,120,294,552,894,1320,1830,2424,3102,3864,4710,5640,

%T 6654,7752,8934,10200,11550,12984,14502,16104,17790,19560,21414,23352,

%U 25374,27480,29670,31944,34302,36744,39270,41880,44574,47352,50214,53160,56190,59304,62502

%N Number of 5-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 >= 7, a(n) = 6*(292 - 90*n + 7*n^2).

%F For n >= 10, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3).

%F G.f.: -6*x^7*(5 + 5*x + 4*x^2)/(-1 + x)^3.

%t Table[If[n < 7, 0, 6 (292 - 90 n + 7 n^2)], {n, 20}]

%t Join[{0, 0, 0, 0, 0, 0}, LinearRecurrence[{3, -3, 1}, {30, 120, 294}, 14]]

%t CoefficientList[Series[-((6 x^6 (5 + 5 x + 4 x^2))/(-1 + x)^3), {x, 0, 20}], x]

%Y Cf. A001105 (3-cycles in the triangular honeycomb obtuse knight graph), A194715 (4-cycles), A290392 (6-cycles).

%K nonn,easy

%O 1,7

%A _Eric W. Weisstein_, Jul 29 2017