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 A291912 Number of 6-cycles in the n X n rook complement graph. 3
 0, 0, 60, 18336, 840800, 14629200, 143939460, 971877760, 5018582016, 21193207200, 76518984300, 243664127520, 699965254560, 1844973808496, 4520720267700, 10403885452800, 22674321863680, 47112768624960, 93845538165276, 180039346960800, 333959821087200, 600947653207440 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS 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 (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1). FORMULA a(n) = (-2 + n)*(-1 + n)^2*n^2*(-52 + 12*n + 76*n^2 - 63*n^3 - 2*n^4 + 20*n^5 - 8*n^6 + n^7)/12. a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13). G.f.: (4 x^3 (-15 - 4389 x - 151778 x^2 - 1277962 x^3 - 3535266 x^4 - 3576650 x^5 - 1293586 x^6 - 137682 x^7 - 1883 x^8 + 11 x^9))/(-1 + x)^13. MATHEMATICA Table[(-2 + n) (-1 + n)^2 n^2 (-52 + 12 n + 76 n^2 - 63 n^3 - 2 n^4 + 20 n^5 - 8 n^6 + n^7)/12, {n, 20}] LinearRecurrence[{13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1}, {0, 0, 60, 18336, 840800, 14629200, 143939460, 971877760, 5018582016, 21193207200, 76518984300, 243664127520, 699965254560}, 20] CoefficientList[Series[(4 x^2 (-15 - 4389 x - 151778 x^2 - 1277962 x^3 - 3535266 x^4 - 3576650 x^5 - 1293586 x^6 - 137682 x^7 - 1883 x^8 + 11 x^9))/(-1 + x)^13, {x, 0, 20}], x] CROSSREFS Cf. A179058 (3-cycles), A291910 (4-cycles), A291911 (5-cycles). Sequence in context: A113424 A009564 A269762 * A001460 A003794 A275051 Adjacent sequences: A291909 A291910 A291911 * A291913 A291914 A291915 KEYWORD nonn AUTHOR Eric W. Weisstein, Sep 05 2017 STATUS approved

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Last modified March 28 13:18 EDT 2023. Contains 361585 sequences. (Running on oeis4.)