|
%I #14 Jun 20 2017 06:55:34
%S 0,0,376,4644,23920,81876,219384,499544,1014160,1885960,3280968,
%T 5402716,8516848,12929804,19034408,27263040,38165376,52323744,
%U 70476456,93380724,121997440,157284564,200461624,252714168,315558528,390435608,479198872,583573276,705791856,847893292
%N Number of 5-cycles in the n X n queen graph.
%H Colin Barker, <a href="/A288916/b288916.txt">Table of n, a(n) for n = 1..1000</a>
%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/QueenGraph.html">Queen Graph</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-7,-4,9,6,-6,-9,4,7,-3,-2,1).
%F G.f.: 4*x^3*(94 + 973*x + 3376*x^2 + 5684*x^3 + 4471*x^4 - 555*x^5 - 4580*x^6 - 4672*x^7 - 2061*x^8 - 426*x^9) / ((1 - x)^7*(1 + x)^4*(1 + x + x^2)). - _Colin Barker_, Jun 19 2017
%t Table[1/2160 (-41575 + 518049 n - 1242186 n^2 + 1172970 n^3 - 485790 n^4 + 73026 n^5 + 576 n^6 - 45 (-1)^n (-867 + 1621 n - 690 n^2 + 74 n^3) + 2560 Cos[(2 n Pi)/3]), {n, 20}]
%t LinearRecurrence[{2, 3, -7, -4, 9, 6, -6, -9, 4, 7, -3, -2, 1}, {0, 0, 376, 4644, 23920, 81876, 219384, 499544, 1014160, 1885960, 3280968, 5402716, 8516848}, 20]
%o (PARI) concat(vector(2), Vec(4*x^3*(94 + 973*x + 3376*x^2 + 5684*x^3 + 4471*x^4 - 555*x^5 - 4580*x^6 - 4672*x^7 - 2061*x^8 - 426*x^9) / ((1 - x)^7*(1 + x)^4*(1 + x + x^2)) + O(x^30))) \\ _Colin Barker_, Jun 19 2017
%Y Cf. A144298 (3-cycles), A156001 (4-cycles), A288917 (6-cycles).
%K nonn,easy
%O 1,3
%A _Eric W. Weisstein_, Jun 19 2017
|
