A288960 Number of 6-cycles in the n X n rook graph.

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

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 A379607 A054331

Adjacent sequences: A288957 A288958 A288959 * A288961 A288962 A288963

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 20 2017

Status

approved