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A288960 Number of 6-cycles in the n X n rook graph. 3
0, 0, 60, 1248, 8400, 35520, 114660, 309120, 731808, 1569600, 3114540, 5802720, 10261680, 17367168, 28310100, 44674560, 68527680, 102522240, 150012828, 215186400, 303208080, 420383040, 574335300, 774204288, 1030860000, 1357137600, 1768092300, 2281275360, 2917032048, 3698822400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..30.

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, Rook Graph

Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

FORMULA

a(n) = (n-1)*(n-2)*n^2*(n+2)*(n^2+2*n-11)/6.

a(n) = 8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*a(n-6)+8*a(n-7)+a(n-8).

G.f.: (12*x^3*(5+64*x+8*x^2-8*x^3+x^4))/(-1+x)^8.

MATHEMATICA

Table[(n - 1) (n - 2) n^2 (n + 2) (n^2 + 2 n - 11)/6, {n, 20}]

Table[Binomial[n, 3] n (n + 2) (n^2 + 2 n - 11), {n, 20}]

LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 0, 60, 1248, 8400, 35520, 114660, 309120}, 20]

CoefficientList[Series[(12 x^2 (5 + 64 x + 8 x^2 - 8 x^3 + x^4))/(-1 + x)^8, {x, 0, 20}], x]

CROSSREFS

Cf. A288961 (3-cycles), A288962 (4-cycles), A288963 (5-cycles).

Sequence in context: A269138 A146347 A289156 * A269196 A054331 A160349

Adjacent sequences:  A288957 A288958 A288959 * A288961 A288962 A288963

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Jun 20 2017

STATUS

approved

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Last modified January 19 09:35 EST 2020. Contains 331048 sequences. (Running on oeis4.)