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 A154949 #14 Nov 13 2022 14:26:04
%S A154949 1,1,3,5,10,18,34,62,115,211,389,715,1316,2420,4452,8188,15061,27701,
%T A154949 50951,93713,172366,317030,583110,1072506,1972647,3628263,6673417,
%U A154949 12274327,22576008,41523752,76374088,140473848,258371689,475219625
%N A154949 Diagonal sums of Riordan array A154948.
%H A154949 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,0,-1,-1)
%F A154949 G.f.: 1/((1-x^2)(1 - x - x^2 - x^3)).
%F A154949 a(n) = sum{k=0..floor(n/2), sum{j=0..n-k+1, C(n-k+1-j,k+1)C(k-1,j)}}.
%F A154949 a(n) = -A000035(n)/2 + A001590(n+4)/2. - _R. J. Mathar_, Oct 25 2012
%t A154949 a=0; b=0; c=0; lst={}; Do[z=a+b+c+1; AppendTo[lst,z]; a=b; b=c; c=z; z=a+b+c; AppendTo[lst,z]; a=b; b=c; c=z,{n,5!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 17 2010 *)
%t A154949 LinearRecurrence[{1,2,0,-1,-1},{1,1,3,5,10},40] (* _Harvey P. Dale_, Nov 13 2022 *)
%K A154949 easy,nonn
%O A154949 0,3
%A A154949 _Paul Barry_, Jan 17 2009