A289707 Number of 6-cycles in the n-triangular honeycomb queen graph.

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

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: A185561 A369583 A283946 * A006089 A260620 A290940

Adjacent sequences: A289704 A289705 A289706 * A289708 A289709 A289710

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 14 2017

Status

approved