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 A356200 #17 Feb 16 2025 08:34:03
%S A356200 3,25,162,969,5613,32062,181989,1030017,5821902,32886505,185714829,
%T A356200 1048619646,5920559661,33426829321,188721717102,1065481514817,
%U A356200 6015458406741,33961820796094,191740095366885,1082517159435249,6111623364952302,34504707439240921
%N A356200 Number of edge covers in the n-gear graph.
%C A356200 Sequence extended to a(1) using the formula/recurrence.
%H A356200 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCover.html">Edge Cover</a>
%H A356200 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GearGraph.html">Gear Graph</a>
%H A356200 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (9,-21,12,-2).
%F A356200 a(n) = (3-sqrt(7))^n + (sqrt(7)+3)^n - Lucas(2*n).
%F A356200 a(n) = 9*a(n-1) - 21*a(n-2) + 12*a(n-3) - 2*a(n-4).
%F A356200 G.f.: x*(3-2*x)/((1-3*x+x^2)*(1-6*x+2*x^2)).
%F A356200 a(n) = 2*A146963(n) - A005248(n). - _R. J. Mathar_, Jan 25 2023
%t A356200 Table[(3 - Sqrt[7])^n + (3 + Sqrt[7])^n - LucasL[2 n], {n, 30}] // Expand
%t A356200 CoefficientList[Series[(3 - 2 x)/((1 - 3 x + x^2) (1 - 6 x + 2 x^2)), {x, 0, 20}], x]
%t A356200 LinearRecurrence[{9, -21, 12, -2}, {3, 25, 162, 969}, 20]
%K A356200 nonn,easy
%O A356200 1,1
%A A356200 _Eric W. Weisstein_, Jul 29 2022