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A288916 Number of 5-cycles in the n X n queen graph. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 20 08:19 EDT 2019. Contains 328253 sequences. (Running on oeis4.)