A288963 Number of 5-cycles in the n X n rook graph.

0, 0, 36, 288, 1320, 4464, 12348, 29568, 63504, 125280, 230868, 402336, 669240, 1070160, 1654380, 2483712, 3634464, 5199552, 7290756, 10041120, 13607496, 18173232, 23951004, 31185792, 40158000, 51186720, 64633140, 80904096, 100455768, 123797520

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 (7, -21, 35, -35, 21, -7, 1).

Formula

a(n) = 6*n*binomial(n,3)*(n^2-2*n+7)/5.

a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7).

G.f.: (-12*x^3*(3+3*x+5*x^2+x^3))/(-1+x)^7.

Mathematica

Table[(n - 2) (n - 1) n^2 (n^2 - 2 n + 7)/5, {n, 20}]
Table[6 n Binomial[n, 3] (n^2 - 2 n + 7)/5, {n, 20}]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 36, 288, 1320, 4464, 12348}, 20]
CoefficientList[Series[-((12 x^2 (3 + 3 x + 5 x^2 + x^3))/(-1 + x)^7), {x, 0, 20}], x]

Crossrefs

Cf. A288961 (3-cycles), A288962 (4-cycles), A288960 (6-cycles).

Sequence in context: A185243 A014136 A245435 * A091081 A017462 A226836

Adjacent sequences: A288960 A288961 A288962 * A288964 A288965 A288966

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 20 2017

Status

approved