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 A099574 #9 Jul 25 2022 01:11:14
%S A099574 1,1,2,2,4,5,9,11,18,23,37,48,74,97,147,195,290,387,568,763,1108,1495,
%T A099574 2152,2915,4167,5662,8047,10962,15506,21168,29825,40787,57280,78448,
%U A099574 109870,150657,210521,288969,403020,553677,770963,1059932,1473898
%N A099574 Diagonal sums of triangle A099573.
%H A099574 G. C. Greubel, <a href="/A099574/b099574.txt">Table of n, a(n) for n = 0..1000</a>
%F A099574 a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..floor(k/2)} binomial(n-k-j, j).
%F A099574 G.f.: (1-x)*(1+x)*(1+x^2) / ( (1-x-x^4)*(1-x^2-x^4) ). - _R. J. Mathar_, Nov 11 2014
%F A099574 From _G. C. Greubel_, Jul 25 2022: (Start)
%F A099574 a(n) = A003269(n+5) - A079977(n+3) - A079977(n+2).
%F A099574 a(n) = A003269(n+5) - A103609(n+5). (End)
%t A099574 a[n_]:= a[n]= Sum[Binomial[n-k-j, j], {k,0,Floor[n/2]}, {j,0,Floor[k/2]}];
%t A099574 Table[a[n], {n, 0, 40}] (* _G. C. Greubel_, Jul 25 2022 *)
%o A099574 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x^4)/((1-x^2-x^4)*(1-x-x^4)) )); // _G. C. Greubel_, Jul 25 2022
%o A099574 (SageMath)
%o A099574 @CachedFunction
%o A099574 def A099574(n): return sum(sum(binomial(n-k-j, j) for j in (0..(k//2))) for k in (0..(n//2)))
%o A099574 [A099574(n) for n in (0..40)] # _G. C. Greubel_, Jul 25 2022
%Y A099574 Cf. A003269, A079977, A099573, A099577, A103609.
%K A099574 easy,nonn
%O A099574 0,3
%A A099574 _Paul Barry_, Oct 23 2004