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 A387571 #4 Sep 02 2025 09:47:51
%S A387571 3,21,64,217,671,2052,6119,18001,52288,150429,429243,1216516,3427659,
%T A387571 9609357,26821696,74576737,206650199,570877956,1572754223,4322192329,
%U A387571 11851475008,32430381861,88576465779,241511251972,657457204371,1787147867397,4851349002304
%N A387571 Number of matchings in the n-double cone graph.
%C A387571 Sequence extended to a(1) using the formula/recurrence.
%H A387571 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DoubleConeGraph.html">Double Cone Graph</a>.
%H A387571 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependentEdgeSet.html">Independent Edge Set</a>.
%H A387571 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,-5,5,-1).
%F A387571 a(n) = 5*a(n-1)-5*a(n-2)-5*a(n-3)+5*a(n-4)-a(n-5).
%F A387571 G.f.: (x*(3+6*x-26*x^2+17*x^3-4*x^4))/((1+x)*(1-3*x+x^2)^2).
%t A387571 Table[2 (-1)^(n + 1) + Fibonacci[2 n + 5] + ((5 - 3 Sqrt[5]) (3 - Sqrt[5])^n + (3 + Sqrt[5])^n (5 + 3 Sqrt[5])) n/(5 2^n) , {n, 0, 20}] // Expand
%t A387571 seq = LinearRecurrence[{5, -5, -5, 5, -1}, {3, 21, 64, 217, 671, 2052}, 20]
%t A387571 CoefficientList[Series[(3 + 6 x - 26 x^2 + 17 x^3 - 4 x^4)/((1 + x) (1 - 3 x + x^2)^2), {x, 0, 20}], x]
%K A387571 nonn,easy,new
%O A387571 1,1
%A A387571 _Eric W. Weisstein_, Sep 02 2025