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 A083580 #10 Dec 28 2023 23:26:00
%S A083580 0,1,3,10,34,114,374,1202,3798,11842,36550,111954,340982,1034210,
%T A083580 3127206,9434866,28419286,85503618,257035142,772219538,2319017910,
%U A083580 6962034466,20896589158,62711787570,188181500054,564640969154
%N A083580 Binomial transform of A083579.
%H A083580 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-16,12).
%F A083580 a(n) = 2*3^n/3-5*0^n/12-(n+1)*2^(n-2).
%F A083580 G.f.: x*(1-4*x+5*x^2)/((1-2*x)^2*(1-3*x)). - _Colin Barker_, Apr 16 2012
%e A083580 a(0) = 2/3-5/12-1/4 = 0 (use 0^0=1).
%t A083580 CoefficientList[Series[x*(1 - 4*x + 5*x^2)/((1 - 2*x)^2*(1 - 3*x)), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Dec 28 2023 *)
%Y A083580 Cf. A083579.
%K A083580 easy,nonn
%O A083580 0,3
%A A083580 _Paul Barry_, May 01 2003