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A288962 Number of 4-cycles in the n X n rook graph. 3
0, 1, 9, 60, 250, 765, 1911, 4144, 8100, 14625, 24805, 39996, 61854, 92365, 133875, 189120, 261256, 353889, 471105, 617500, 798210, 1018941, 1285999, 1606320, 1987500, 2437825, 2966301, 3582684, 4297510, 5122125, 6068715, 7150336, 8380944, 9775425, 11349625, 13120380, 15105546, 17324029, 19795815, 22542000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..40.

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 (6, -15, 20, -15, 6, -1).

FORMULA

a(n) = n*binomial(n,2)*(n^2-4*n+5)/2.

a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6).

G.f.: (x^2*(1+3*x+21*x^2+5*x^3))/(-1+x)^6.

MATHEMATICA

Table[n^2 (n - 1) (n^2 - 4 n + 5)/4, {n, 20}]

Table[n Binomial[n, 2] (n^2 - 4 n + 5)/2, {n, 20}]

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 1, 9, 60, 250, 765}, 20]

CoefficientList[Series[(x (1 + 3 x + 21 x^2 + 5 x^3))/(-1 + x)^6, {x, 0, 20}], x]

PROG

(MAGMA) [n^2*(n-1)*(n^2-4*n+5)/4 : n in [1..50]]; // Wesley Ivan Hurt, Apr 23 2021

CROSSREFS

Cf. A288961 (3-cycles), A288963 (5-cycles), A288960 (6-cycles).

Sequence in context: A098327 A118674 A268972 * A074431 A268965 A081904

Adjacent sequences:  A288959 A288960 A288961 * A288963 A288964 A288965

KEYWORD

nonn,easy,changed

AUTHOR

Eric W. Weisstein, Jun 20 2017

STATUS

approved

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Last modified May 6 01:51 EDT 2021. Contains 343579 sequences. (Running on oeis4.)