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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
OFFSET
1,3
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Rook Graph
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 20 2017
STATUS
approved