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 A053209 #36 Oct 27 2023 22:00:45
%S A053209 1,5,14,32,68,140,284,572,1148,2300,4604,9212,18428,36860,73724,
%T A053209 147452,294908,589820,1179644,2359292,4718588,9437180,18874364,
%U A053209 37748732,75497468,150994940,301989884,603979772,1207959548,2415919100
%N A053209 Row sums of A051598.
%H A053209 G. C. Greubel, <a href="/A053209/b053209.txt">Table of n, a(n) for n = 0..1000</a>
%H A053209 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A053209 a(0) = 1, a(1) = 5, a(n+1) = 2*a(n) + 4, for n >= 1.
%F A053209 a(n) = 9*2^(n-1) - 4, n >= 1.
%F A053209 a(n) = 4*n + Sum[i = 0, n - 1] a(i). - _Jon Perry_, Nov 20 2012
%F A053209 a(n) = A048491(n)/2, n>0. - _Philippe Deléham_, Apr 15 2013
%F A053209 G.f.: (1+x)^2/((1-x)*(1-2*x)). - _Philippe Deléham_, Apr 15 2013
%F A053209 a(n) = 3*a(n-1) - 2*a(n-2) with a(0)=1, a(1)=5, a(2)=14. - _Philippe Deléham_, Apr 15 2013
%F A053209 E.g.f.: (1 - 8*exp(x) + 9*exp(2*x))/2. - _Stefano Spezia_, Sep 28 2022
%t A053209 Join[{1}, LinearRecurrence[{3, -2}, {5, 14}, 50]] (* _G. C. Greubel_, Sep 03 2018 *)
%o A053209 (PARI) m=30; v=concat([5,14], vector(m-2)); for(n=3, m, v[n] = 3*v[n-1] -2*v[n-2]); concat([1], v) \\ _G. C. Greubel_, Sep 03 2018
%o A053209 (Magma) I:=[5,14]; [1] cat [n le 2 select I[n] else 3*Self(n-1) - 2*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Sep 03 2018
%o A053209 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)^2)/((1-x)*(1-2*x))); // _Marius A. Burtea_, Oct 15 2019
%Y A053209 Cf. A051598, A053208.
%Y A053209 Cf. A083329, A131051.
%Y A053209 Cf. A048491.
%K A053209 nonn,easy
%O A053209 0,2
%A A053209 _Asher Auel_, Dec 14 1999