This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A289706 #20 Feb 16 2025 08:33:49
%S A289706 0,0,24,324,1692,5796,15516,35388,71988,134460,234972,389304,617400,
%T A289706 943992,1399272,2019528,2847960,3935304,5340816,7132860,9390084,
%U A289706 12201948,15670116,19908900,25046892,31227300,38609844,47370960,57705984,69829200,83976336,100404432
%N A289706 Number of 5-cycles in the n-triangular honeycomb queen graph.
%H A289706 Colin Barker, <a href="/A289706/b289706.txt">Table of n, a(n) for n = 1..1000</a>
%H A289706 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A289706 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (4, -3, -8, 14, 0, -14, 8, 3, -4, 1).
%F A289706 a(n) = (1095 - 4770*n + 934*n^2 + 4680*n^3 - 3170*n^4 + 540*n^5 +
%F A289706 16*n^6 - 15*(-1)^n (73 - 30*n + 2*n^2))/320.
%F A289706 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).
%F A289706 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
%t A289706 Table[(1095 - 4770 n + 934 n^2 + 4680 n^3 - 3170 n^4 + 540 n^5 +
%t A289706 16 n^6 - 15 (-1)^n (73 - 30 n + 2 n^2))/320, {n, 20}]
%t A289706 LinearRecurrence[{4, -3, -8, 14, 0, -14, 8, 3, -4, 1}, {0, 0, 24, 324, 1692, 5796, 15516, 35388, 71988, 134460}, 20]
%o A289706 (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
%Y A289706 Cf. A105636 (3-cycles), A289705 (4-cycles), A289707 (6-cycles).
%K A289706 nonn,easy
%O A289706 1,3
%A A289706 _Eric W. Weisstein_, Jul 14 2017