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 A374096 #23 Jan 22 2025 07:49:20
%S A374096 1,4,16,59,214,768,2745,9792,34900,124339,442906,1577540,5618665,
%T A374096 20011452,71272296,253840779,904068526,3219889720,11467810393,
%U A374096 40843217384,145465283884,518082304131,1845177508818,6571697181084,23405446635913,83359734391300,296890096642144
%N A374096 Number of edge covers of fan graph F_{1,n}.
%H A374096 Paolo Xausa, <a href="/A374096/b374096.txt">Table of n, a(n) for n = 1..1000</a>
%H A374096 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FanGraph.html">Fan Graph</a>
%H A374096 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,-5,-2).
%F A374096 a(n) = 4*a(n-1)-5*a(n-3)-2*a(n-4).
%F A374096 G.f.: x/((1 - x - x^2)*(1 - 3*x - 2*x^2)). - _Stefano Spezia_, Jun 29 2024
%F A374096 a(n) = A007483(n-1) - A212804(n). - _R. J. Mathar_, Jun 29 2024
%e A374096 The fan graph F_{1,2} is the cycle with three vertices and has 4 edge covers.
%e A374096 The graph F_{1,3} is formed by adding a chord to the cycle with four vertices. The cycle C_4 has 7 edge covers, so there are 7 edge covers of F_{1,3} without the chord. If the chord is there, the two endpoints are covered. To cover the remaining two vertices, we need at least one of the two edges on each side of each vertex, giving us 3*3 choices total. So we have 16 edge covers for F_{1,3}.
%e A374096 We interpret F_{1,1} to be the path with two vertices with one edge cover.
%t A374096 LinearRecurrence[{4, 0, -5, -2}, {1, 4, 16, 59}, 30] (* _Paolo Xausa_, Jan 22 2025 *)
%K A374096 nonn,easy
%O A374096 1,2
%A A374096 _Feryal Alayont_, Jun 28 2024