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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
OFFSET
1,3
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jul 14 2017
STATUS
approved