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 A089143 #16 May 24 2025 16:22:35
%S A089143 3,12,30,66,138,282,570,1146,2298,4602,9210,18426,36858,73722,147450,
%T A089143 294906,589818,1179642,2359290,4718586,9437178,18874362,37748730,
%U A089143 75497466,150994938,301989882,603979770,1207959546,2415919098,4831838202,9663676410,19327352826
%N A089143 a(n) = 9*2^n - 6.
%H A089143 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A089143 a(n) = 3*A033484(n).
%F A089143 From _Elmo R. Oliveira_, May 24 2025: (Start)
%F A089143 G.f.: 3*(x+1)/((x-1)*(2*x-1)).
%F A089143 E.g.f.: 3*exp(x)*(3*exp(x) - 2).
%F A089143 a(n) = 3*a(n-1) - 2*a(n-2). (End)
%t A089143 a=3; lst={a}; k=9; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 16 2008 *)
%t A089143 9*2^Range[0,40]-6 (* _Harvey P. Dale_, Sep 15 2013 *)
%o A089143 (PARI) my(x='x+O('x^32)); Vec(3*(1+x)/(1-3*x+2*x^2)) \\ _Elmo R. Oliveira_, May 24 2025
%Y A089143 Cf. A033484.
%K A089143 nonn,easy
%O A089143 0,1
%A A089143 _Parthasarathy Nambi_, Sep 21 2004