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 A387570 #4 Sep 02 2025 09:23:43
%S A387570 2,3,9,22,51,111,234,477,951,1858,3573,6777,12706,23583,43389,79214,
%T A387570 143631,258843,463914,827337,1468827,2597018,4574529,8030037,14050946,
%U A387570 24514011,42651729,74021062,128157771,221397543,381680298,656721237,1127890911,1933765618
%N A387570 Number of matchings in the n-dipyramidal graph.
%C A387570 Sequence extended to n = 0 using formula/recurrence.
%H A387570 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DipyramidalGraph.html">Dipyramidal Graph</a>.
%H A387570 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependentEdgeSet.html">Independent Edge Set</a>.
%H A387570 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-5,0,3,1).
%F A387570 a(n) = (n^2 + 5)*LucasL(n) + 9*n*Fibonacci(n))/5.
%F A387570 a(n) = 3*a(n-1)-5*a(n-3)+3*a(n-5)+a(n-6).
%F A387570 G.f.: (-2+3*x-5*x^3+3*x^5)/(-1+x+x^2)^3.
%t A387570 Table[((n^2 + 5) LucasL[n] + 9 n Fibonacci[n])/5, {n, 0, 20}]
%t A387570 LinearRecurrence[{3, 0, -5, 0, 3, 1}, {3, 9, 22, 51, 111, 234}, {0, 20}]
%t A387570 CoefficientList[Series[(-2 + 3 x - 5 x^3 + 3 x^5)/(-1 + x + x^2)^3, {x, 0, 20}], x]
%K A387570 nonn,easy,new
%O A387570 0,1
%A A387570 _Eric W. Weisstein_, Sep 02 2025