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A288963 Number of 5-cycles in the n X n rook graph. 3
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 (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 (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

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Last modified January 24 16:47 EST 2020. Contains 331209 sequences. (Running on oeis4.)