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 A290031 #18 Feb 16 2025 08:33:49
%S A290031 0,0,0,16,128,640,2560,8960,28672,86016,245760,675840,1802240,4685824,
%T A290031 11927552,29818880,73400320,178257920,427819008,1016070144,2390753280,
%U A290031 5578424320,12918456320,29712449536,67914170368,154350387200,348966092800,785173708800,1758789107712
%N A290031 Number of 6-cycles in the n-hypercube graph.
%H A290031 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>.
%H A290031 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>.
%H A290031 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-24,32,-16).
%F A290031 a(n) = 2^(n + 1)*binomial(n, 3).
%F A290031 a(n) = 8*a(n-1)-24*a(n-2)+32*a(n-4)-16*a(n-4).
%F A290031 G.f.: (16*x^3)/(-1 + 2*x)^4.
%F A290031 From _Amiram Eldar_, Jan 05 2022: (Start)
%F A290031 Sum_{n>=3} 1/a(n) = 3*(2*log(2)-1)/16.
%F A290031 Sum_{n>=3} (-1)^(n+1)/a(n) = (3/2)^3*log(3/2) - 21/16. (End)
%t A290031 Table[2^(n + 1) Binomial[n, 3], {n, 0, 20}]
%t A290031 LinearRecurrence[{8, -24, 32, -16}, {0, 0, 0, 16}, 20]
%t A290031 CoefficientList[Series[(16 x^3)/(-1 + 2 x)^4, {x, 0, 20}], x]
%t A290031 Table[Length[FindCycle[HypercubeGraph[n], {6}, All]], {n, 0, 10}] (* _Eric W. Weisstein_, Aug 02 2023 *)
%o A290031 (Magma) [2^(n + 1)*Binomial(n, 3): n in [0..30]]; // _Wesley Ivan Hurt_, Apr 21 2021
%Y A290031 Cf. A001788 (4-cycles).
%Y A290031 Cf. A364688 (8-cycles).
%K A290031 nonn
%O A290031 0,4
%A A290031 _Eric W. Weisstein_, Jul 17 2017