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
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).
Programs
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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] -
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
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