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A291910 Number of 4-cycles in the n X n rook complement graph. 3
0, 0, 9, 576, 6900, 44100, 196245, 686784, 2023056, 5232600, 12224025, 26310240, 52936884, 100663836, 182452725, 317318400, 532407360, 865571184, 1368508041, 2110550400, 3183182100, 4705372980, 6829824309, 9750223296, 13709610000, 19009965000, 26023131225 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..27.

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, Rook Complement Graph

Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

FORMULA

a(n) = (n-2)*(n-1)^2*n^2*(-4 + 5*n - 4*n^2 + n^3)/8.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9).

G.f.: -((3 x^3 (3 + 165 x + 680 x^2 + 660 x^3 + 165 x^4 + 7 x^5))/(-1 + x)^9).

MATHEMATICA

Table[(-2 + n) (-1 + n)^2 n^2 (-4 + 5 n - 4 n^2 + n^3)/8, {n, 20}]

LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {0, 0, 9, 576, 6900, 44100, 196245, 686784, 2023056}, 30]

CoefficientList[Series[-((3 x^2 (3 + 165 x + 680 x^2 + 660 x^3 + 165 x^4 + 7 x^5))/(-1 + x)^9), {x, 0, 20}], x]

CROSSREFS

Cf. A179058 (3-cycles), A291911 (5-cycles), A291912 (6-cycles).

Sequence in context: A267548 A326614 A347844 * A074731 A064560 A264121

Adjacent sequences:  A291907 A291908 A291909 * A291911 A291912 A291913

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Sep 05 2017

STATUS

approved

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Last modified May 25 02:50 EDT 2022. Contains 354047 sequences. (Running on oeis4.)