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 A364605 #32 Jun 21 2025 01:57:00
%S A364605 0,0,0,0,5,44,147,464,1236,3100,7293,16472,35919,76216,158040,321472,
%T A364605 643229,1268868,2472147,4764120,9092300,17202636,32294277,60199088,
%U A364605 111498175,205306192,376014960,685273120,1243205205,2245893340,4041415347,7245914176,12947137412
%N A364605 Number of 6-cycles in the n-Lucas cube graph.
%H A364605 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A364605 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LucasCubeGraph.html">Lucas Cube Graph</a>
%H A364605 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-8,5,8,-2,-4,-1).
%F A364605 a(n) = (n + 1)*(3*(40n^2 - 145*n + 99)*A000045(n) - (40*n^2 - 133*n + 75)*A000032(n))/150.
%F A364605 a(n) = 4*a(n-1) - 2*a(n-2) - 8*a(n-3) + 5*a(n-4) + 8*a(n-5) - 2*a(n-6) - 4*a(n-7) - a(n-8) for n > 1.
%F A364605 G.f.: x^4*(5+24*x-19*x^2+4*x^3+x^4)/(-1+x+x^2)^4.
%t A364605 Join[{0}, Table[(n + 1) (3 (40 n^2 - 145 n + 99) Fibonacci[n] - (40 n^2 - 133 n + 75) LucasL[n])/150, {n, 20}]]
%t A364605 Join[{0}, LinearRecurrence[{4, -2, -8, 5, 8, -2, -4, -1}, {0, 0, 0, 5, 44, 147, 464, 1236}, 20]]
%t A364605 CoefficientList[Series[x^4 (5 + 24 x - 19 x^2 + 4 x^3 + x^4)/(-1 + x + x^2)^4, {x, 0, 20}], x]
%Y A364605 Cf. A245961 (number of 4-cycles).
%K A364605 nonn,easy
%O A364605 1,5
%A A364605 _Eric W. Weisstein_, Jul 30 2023