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