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 A134238 #32 Apr 05 2025 23:18:04
%S A134238 1,5,14,28,47,71,100,134,173,217,266,320,379,443,512,586,665,749,838,
%T A134238 932,1031,1135,1244,1358,1477,1601,1730,1864,2003,2147,2296,2450,2609,
%U A134238 2773,2942,3116,3295,3479,3668,3862,4061,4265,4474,4688,4907,5131,5360,5594,5833,6077
%N A134238 Row sums of triangle A134237.
%H A134238 Andrew Howroyd, <a href="/A134238/b134238.txt">Table of n, a(n) for n = 1..1000</a>
%H A134238 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A134238 Binomial transform of (1, 4, 5, 0, 0, 0, ...).
%F A134238 a(n) = a(n-1) + 5*n - 6 (with a(1)=1). - _Vincenzo Librandi_, Nov 23 2010
%F A134238 a(n) = (5*n^2 - 7*n + 4)/2. - _Charles R Greathouse IV_, Jun 17 2017
%F A134238 From _Elmo R. Oliveira_, Feb 08 2025: (Start)
%F A134238 G.f.: x*(2*x^2 + 2*x + 1)/(1-x)^3.
%F A134238 E.g.f.: exp(x)*(5*x^2 - 2*x + 4)/2 - 2.
%F A134238 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 4. (End)
%t A134238 LinearRecurrence[{3,-3,1},{1,5,14},50] (* or *) Rest[CoefficientList[Series[x*(2*x^2 + 2*x + 1)/(1-x)^3,{x,0,50}],x]] (* _James C. McMahon_, Apr 05 2025 *)
%o A134238 (PARI) a(n)=(5*n^2-7*n+4)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A134238 Cf. A134237.
%K A134238 nonn,easy
%O A134238 1,2
%A A134238 _Gary W. Adamson_, Oct 14 2007
%E A134238 a(47) onwards from _Andrew Howroyd_, Feb 08 2025