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A291911 Number of 5-cycles in the n X n rook complement graph. 3
0, 0, 36, 3456, 77040, 800640, 5265540, 25514496, 99320256, 327836160, 951285060, 2488844160, 5980596336, 13384215936, 28197301860, 56398325760, 107825391360, 198142765056, 351580800996, 604675808640, 1011282960240, 1649187872640, 2628701385156 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..23.

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 (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).

FORMULA

a(n) = (n - 2)^2*(n - 1)^2*n^2*(4 + 2*n + 3*n^2 - 4*n^3 + n^4)/10.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11).

G.f.: -((36 x^3 (1 + 85 x + 1139 x^2 + 3815 x^3 + 3815 x^4 + 1139 x^5 + 85 x^6 + x^7))/(-1 + x)^11).

MATHEMATICA

Table[(n - 2)^2 (n - 1)^2 n^2 (4 + 2 n + 3 n^2 - 4 n^3 + n^4)/10, {n, 20}]

LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {0, 0, 36, 3456, 77040, 800640, 5265540, 25514496, 99320256, 327836160, 951285060}, 20]

CoefficientList[Series[-((36 x^2 (1 + 85 x + 1139 x^2 + 3815 x^3 + 3815 x^4 + 1139 x^5 + 85 x^6 + x^7))/(-1 + x)^11), {x, 0, 20}], x]

CROSSREFS

Cf. A179058 (3-cycles), A291910 (4-cycles), A291912 (6-cycles).

Sequence in context: A338076 A303339 A034983 * A072377 A209267 A120349

Adjacent sequences: A291908 A291909 A291910 * A291912 A291913 A291914

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Sep 05 2017

STATUS

approved

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Last modified February 7 15:43 EST 2023. Contains 360127 sequences. (Running on oeis4.)