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 A289706 Number of 5-cycles in the n-triangular honeycomb queen graph. 4
 0, 0, 24, 324, 1692, 5796, 15516, 35388, 71988, 134460, 234972, 389304, 617400, 943992, 1399272, 2019528, 2847960, 3935304, 5340816, 7132860, 9390084, 12201948, 15670116, 19908900, 25046892, 31227300, 38609844, 47370960, 57705984, 69829200, 83976336, 100404432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Graph Cycle Index entries for linear recurrences with constant coefficients, signature (4, -3, -8, 14, 0, -14, 8, 3, -4, 1). FORMULA a(n) = (1095 - 4770*n + 934*n^2 + 4680*n^3 - 3170*n^4 + 540*n^5 +     16*n^6 - 15*(-1)^n (73 - 30*n + 2*n^2))/320. a(n) = 4*a(n-1) - 3*a(n-2) - 8*a(n-3) + 14*a(n-4) - 14*a(n-6) + 8*a(n-7) + 3*a(n-8) - 4*a(n-9) + a(n-10). G.f.: 12*x^3*(2 + 19*x + 39*x^2 + 16*x^3 - 28*x^4 - 24*x^5) / ((1 - x)^7*(1 + x)^3). - Colin Barker, Aug 07 2017 MATHEMATICA Table[(1095 - 4770 n + 934 n^2 + 4680 n^3 - 3170 n^4 + 540 n^5 +     16 n^6 - 15 (-1)^n (73 - 30 n + 2 n^2))/320, {n, 20}] LinearRecurrence[{4, -3, -8, 14, 0, -14, 8, 3, -4, 1}, {0, 0, 24, 324, 1692, 5796, 15516, 35388, 71988, 134460}, 20] PROG (PARI) concat(vector(2), Vec(12*x^3*(2 + 19*x + 39*x^2 + 16*x^3 - 28*x^4 - 24*x^5) / ((1 - x)^7*(1 + x)^3) + O(x^50))) \\ Colin Barker, Aug 07 2017 CROSSREFS Cf. A105636 (3-cycles), A289705 (4-cycles), A289707 (6-cycles). Sequence in context: A288507 A199301 A239793 * A300846 A006922 A036221 Adjacent sequences:  A289703 A289704 A289705 * A289707 A289708 A289709 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Jul 14 2017 STATUS approved

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Last modified April 23 03:11 EDT 2021. Contains 343198 sequences. (Running on oeis4.)