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 A288961 Number of 3-cycles in the n X n rook graph. 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1000 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 (5,-10,10,-5,1). 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). Sequence in context: A177082 A296196 A211918 * A090382 A102359 A000397 Adjacent sequences:  A288958 A288959 A288960 * A288962 A288963 A288964 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Jun 20 2017 EXTENSIONS Terms a(31) and beyond from Andrew Howroyd, Apr 26 2020 STATUS approved

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Last modified May 13 19:36 EDT 2021. Contains 343868 sequences. (Running on oeis4.)