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 A100217 #8 Mar 28 2024 09:03:58
%S A100217 1,1,4,12,42,149,543,2007,7501,28265,107196,408653,1564506,6010964,
%T A100217 23164467,89501021,346588092,1344804060,5227147969,20349230347,
%U A100217 79330194097,309653982738,1210071825851,4733665388134,18535196846866
%N A100217 Diagonal sums of a binomial number triangle.
%C A100217 Diagonal sums of A100100.
%H A100217 G. C. Greubel, <a href="/A100217/b100217.txt">Table of n, a(n) for n = 0..1000</a>
%F A100217 a(n) = Sum_{k=0..floor(n/2)} binomial(2*n-3*k-1, n-2*k).
%t A100217 A100217[n_]:= Sum[Binomial[2*n-3*k-1,n-2*k], {k,0,Floor[n/2]}];
%t A100217 Table[A100217[n], {n,0,40}] (* _G. C. Greubel_, Mar 28 2024 *)
%o A100217 (Magma) [(&+[Binomial(2*n-3*k-1, n-2*k): k in [0..Floor(n/2)]]): n in [0..40]]; // _G. C. Greubel_, Mar 28 2024
%o A100217 (SageMath) [sum(binomial(2*n-3*k-1, n-2*k) for k in range(1+n//2)) for n in range(41)] # _G. C. Greubel_, Mar 28 2024
%Y A100217 Cf. A100100.
%K A100217 easy,nonn
%O A100217 0,3
%A A100217 _Paul Barry_, Nov 08 2004