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 A367967 #11 Feb 16 2025 08:34:06
%S A367967 0,0,3,27,126,462,1521,4761,14556,44028,132543,398199,1195290,3586698,
%T A367967 10761069,32284341,96854328,290564472,871695099,2615087187,7845263670,
%U A367967 23535793350,70607382633,211822150737,635466455316,1906399369332,5719198111671,17157594338991
%N A367967 a(n) = 3/4*(3^(n + 1) - 2*n - 4*n^2 - 3).
%C A367967 Number of 5-cycles in the n-Dorogovtsev-Goltsev-Mendes graph (using the convention that DGM(0) = P_2).
%H A367967 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Dorogovtsev-Goltsev-MendesGraph.html">Dorogovtsev-Goltsev-Mendes Graph</a>.
%H A367967 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>.
%H A367967 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,10,-3).
%F A367967 a(n) = 3/4*(3^(n + 1) - 2*n - 4*n^2 - 3).
%F A367967 a(n) = 6*a(n-1) - 12*a(n-2) + 10*a(n-3) - 3*a(n-4).
%F A367967 G.f.: 3*x^2*(1+3*x)/((-1+x)^3*(-1+3*x)).
%t A367967 Table[3/4 (3^(n + 1) - 2 n - 4 n^2 - 3), {n, 0, 20}]
%t A367967 LinearRecurrence[{6, -12, 10, -3}, {0, 0, 3, 27}, 20]
%t A367967 CoefficientList[Series[3 x^2 (1 + 3 x)/((-1 + x)^3 (-1 + 3 x)), {x, 0, 20}], x]
%Y A367967 Cf. A003462(n) (3-cycles), A290764(n-1) (4-cycles), A367968(n) (6-cycles).
%K A367967 nonn,easy
%O A367967 0,3
%A A367967 _Eric W. Weisstein_, Dec 06 2023