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 A190089 #24 Sep 08 2022 08:45:56
%S A190089 1,4,21,114,616,3329,17991,97229,525456,2839729,15346786,82938844,
%T A190089 448227521,2422362079,13091204281,70748973084,382349636061,
%U A190089 2066337330754,11167134898976,60350698792449,326154101090951,1762639037938629,9525854090667496,51480702630305689,278217860370802066
%N A190089 Row sums of the triangular matrix A190088.
%H A190089 G. C. Greubel, <a href="/A190089/b190089.txt">Table of n, a(n) for n = 0..1350</a> (terms 0..136 from Vincenzo Librandi)
%H A190089 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,2,1).
%F A190089 a(n) = Sum_{k=0..n} binomial(3*n-k+1,3*n-3*k+1).
%F A190089 G.f.: (1-x-x^2)/(1-5*x-2*x^2-x^3).
%F A190089 a(n) = 5*a(n-1)+2*a(n-2)+a(n-3) and a(0)=1, a(1)=4, a(2)=21. - _Harvey P. Dale_, Sep 18 2013
%t A190089 Table[Sum[Binomial[3n - k + 1, 3n - 3k + 1], {k, 0, n}], {n, 0, 12}]
%t A190089 LinearRecurrence[{5,2,1},{1,4,21},30] (* _Harvey P. Dale_, Sep 18 2013 *)
%o A190089 (Maxima) makelist(sum(binomial(3*n-k+1,3*n-3*k+1),k,0,n),n,0,24);
%o A190089 (PARI) Vec((1-x-x^2)/(1-5*x-2*x^2-x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Jun 30 2011
%o A190089 (Magma) [(&+[Binomial(3*n-k+1,3*n-3*k+1): k in [0..n]]): n in [0..30]]; // _G. C. Greubel_, Mar 04 2018
%Y A190089 Cf. A190088, A190090.
%K A190089 nonn,easy
%O A190089 0,2
%A A190089 _Emanuele Munarini_, May 04 2011