A288916 Number of 5-cycles in the n X n queen graph.

0, 0, 376, 4644, 23920, 81876, 219384, 499544, 1014160, 1885960, 3280968, 5402716, 8516848, 12929804, 19034408, 27263040, 38165376, 52323744, 70476456, 93380724, 121997440, 157284564, 200461624, 252714168, 315558528, 390435608, 479198872, 583573276, 705791856, 847893292

Offset

1,3

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, Queen Graph

Index entries for linear recurrences with constant coefficients, signature (2,3,-7,-4,9,6,-6,-9,4,7,-3,-2,1).

Formula

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

Mathematica

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}]
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]

Prog

(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

Crossrefs

Cf. A144298 (3-cycles), A156001 (4-cycles), A288917 (6-cycles).

Sequence in context: A188007 A251644 A234916 * A198640 A171489 A105717

Adjacent sequences: A288913 A288914 A288915 * A288917 A288918 A288919

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 19 2017

Status

approved