A289706 Number of 5-cycles in the n-triangular honeycomb queen graph.

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

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