login
A288961
Number of 3-cycles in the n X n rook graph.
6
0, 0, 6, 32, 100, 240, 490, 896, 1512, 2400, 3630, 5280, 7436, 10192, 13650, 17920, 23120, 29376, 36822, 45600, 55860, 67760, 81466, 97152, 115000, 135200, 157950, 183456, 211932, 243600, 278690, 317440, 360096, 406912, 458150, 514080, 574980, 641136, 712842, 790400
OFFSET
1,3
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Rook Graph
FORMULA
a(n) = 2*n*binomial(n,3).
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5).
G.f.: (-2*x^3*(3+x))/(-1+x)^5.
MATHEMATICA
Table[n^2 (n - 1) (n - 2)/3, {n, 20}]
Table[2 n Binomial[n, 3], {n, 20}]
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 6, 32, 100}, 20]
CoefficientList[Series[-((2 x^2 (3 + x))/(-1 + x)^5), {x, 0, 20}], x]
PROG
(PARI) a(n) = {2*n*binomial(n, 3)} \\ Andrew Howroyd, Apr 26 2020
CROSSREFS
Cf. A288962 (4-cycles), A288963 (5-cycles), A288960 (6-cycles).
Main diagonal of A360855.
Sequence in context: A177082 A296196 A211918 * A090382 A360839 A102359
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 20 2017
EXTENSIONS
Terms a(31) and beyond from Andrew Howroyd, Apr 26 2020
STATUS
approved