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 A364688 #8 Feb 16 2025 08:34:06
%S A364688 0,0,0,6,696,6720,39840,184800,736512,2644992,8801280,27624960,
%T A364688 82790400,238977024,668688384,1822679040,4858183680,12700876800,
%U A364688 32647938048,82682707968,206650736640,510425825280,1247438438400,3019527684096,7245593051136,17248655769600
%N A364688 Number of 8-cycles in the hypercube graph Q_n.
%H A364688 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A364688 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>
%H A364688 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (10,-40,80,-80,32).
%F A364688 a(n) = 2^(n - 4)*n*(n - 1)*(n - 2)*(27*n - 79).
%F A364688 a(n) = 10*a(n-1) - 40*a(n-2) + 80*a(n-3) - 80*a(n-4) + 32*a(n-5).
%F A364688 G.f.: -6*x^3*(1 + 106*x)/(-1 + 2*x)^5.
%t A364688 Table[Length[FindCycle[HypercubeGraph[n], {8}, All]], {n, 0, 9}]
%t A364688 Table[2^(n - 4) n (n - 1) (n - 2) (27 n - 79), {n, 0, 20}]
%t A364688 Table[3 2^(n - 3) Binomial[n, 3] (27 n - 79), {n, 0, 20}]
%t A364688 LinearRecurrence[{10, -40, 80, -80, 32}, {0, 0, 0, 6, 696}, 20]
%t A364688 CoefficientList[Series[6 x^3 (1 + 106 x)/(1 - 2 x)^5, {x, 0, 20}], x]
%Y A364688 Cf. A001788 (4-cycles).
%Y A364688 Cf. A290031 (6-cycles).
%K A364688 nonn
%O A364688 0,4
%A A364688 _Eric W. Weisstein_, Aug 02 2023