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 A289707 Number of 6-cycles in the n-triangular honeycomb queen graph. 4
 0, 0, 16, 911, 8013, 38130, 129932, 358272, 851710, 1815124, 3554910, 6510729, 11289019, 18704640, 29823436, 46014402, 69002190, 100930284, 144424446, 202667301, 279473821, 379377584, 507719550, 670746120, 875712560, 1130992902, 1446199474, 1832304547, 2301777585, 2868718404 (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 (3, 1, -10, 3, 13, -3, -12, -3, 13, 3, -10, 1, 3, -1). FORMULA a(n) = 3*a(n-1)+a(n-2)-10*a(n-3)+3*a(n-4)+13*a(n-5)-3*a(n-6)-12*a(n-7)-3*a(n-8)+13*a(n-9)+3*a(n-10)-10*a(n-11)+a(n-12)+3*a(n-13)-a(n-14). G.f.: x^3*(16 + 863*x + 5264*x^2 + 13340*x^3 + 16591*x^4 + 7535*x^5 - 7572*x^6 - 14592*x^7 - 9919*x^8 - 2886*x^9) / ((1 - x)^8*(1 + x)^4*(1 + x + x^2)). - Colin Barker, Jul 27 2017 MATHEMATICA Table[(-315 (-1)^n (-2489 + 1659 n - 297 n^2 + 10 n^3) - 792995 + 3789081 n - 1968939 n^2 - 3033450 n^3 + 3489990 n^4 - 1269366 n^5 + 154014 n^6 + 1440 n^7 + 8960 Cos[2 n Pi/3] - 8960 Sqrt[3] Sin[2 n Pi/3])/40320, {n, 20}] LinearRecurrence[{3, 1, -10, 3, 13, -3, -12, -3, 13, 3, -10, 1, 3, -1}, {0, 0, 16, 911, 8013, 38130, 129932, 358272, 851710, 1815124, 3554910, 6510729, 11289019, 18704640}, 20] PROG (PARI) concat(vector(2), Vec(x^3*(16 + 863*x + 5264*x^2 + 13340*x^3 + 16591*x^4 + 7535*x^5 - 7572*x^6 - 14592*x^7 - 9919*x^8 - 2886*x^9) / ((1 - x)^8*(1 + x)^4*(1 + x + x^2)) + O(x^60))) \\ Colin Barker, Jul 27 2017 CROSSREFS Cf. A105636 (3-cycles), A289705 (4-cycles), A289706 (5-cycles). Sequence in context: A214386 A185561 A283946 * A006089 A260620 A290940 Adjacent sequences:  A289704 A289705 A289706 * A289708 A289709 A289710 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Jul 14 2017 STATUS approved

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Last modified August 17 00:01 EDT 2022. Contains 356180 sequences. (Running on oeis4.)