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 A122120 #23 Sep 15 2024 06:50:42
%S A122120 1,3,21,111,633,3531,19821,111063,622641,3490131,19564293,109668351,
%T A122120 614752041,3446023323,19316861661,108281656551,606978381153,
%U A122120 3402448433571,19072599164661,106912432560783,599303122725081
%N A122120 a(n) = 4*a(n-1) + 9*a(n-2), for n>1, with a(0)=1, a(1)=3.
%H A122120 G. C. Greubel, <a href="/A122120/b122120.txt">Table of n, a(n) for n = 0..1000</a>
%H A122120 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,9).
%F A122120 a(n) = Sum_{k=0..n} 3^(n-k)*A055380(n,k).
%F A122120 G.f.: (1-x)/(1-4*x-9*x^2).
%F A122120 Limit_{n -> oo} a(n+1)/a(n) = 2 + sqrt(13).
%t A122120 CoefficientList[Series[(1-x)/(1-4*x-9*x^2), {x, 0, 30}], x] (* _G. C. Greubel_, Feb 26 2019 *)
%t A122120 nxt[{a_,b_}]:={b,4b+9a}; NestList[nxt,{1,3},20][[All,1]] (* or *) LinearRecurrence[{4,9},{1,3},30] (* _Harvey P. Dale_, Oct 06 2020 *)
%o A122120 (PARI) my(x='x+O('x^30)); Vec((1-x)/(1-4*x-9*x^2)) \\ _G. C. Greubel_, Feb 26 2019
%o A122120 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-x)/(1-4*x-9*x^2) )); // _G. C. Greubel_, Feb 26 2019
%o A122120 (Sage) ((1-x)/(1-4*x-9*x^2)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Feb 26 2019
%Y A122120 First differences of A015533.
%Y A122120 Binomial transform of A091914.
%K A122120 nonn,easy
%O A122120 0,2
%A A122120 _Philippe Deléham_, Oct 19 2006