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%I #8 Sep 08 2022 08:45:28
%S 1,1,1,2,3,5,8,13,22,36,61,102,172,292,493,841,1429,2439,4169,7124,
%T 12216,20930,35940,61749,106155,182749,314638,542338,935195,1613593,
%U 2786037,4811920,8316435,14378247,24870062,43036264,74496224,129008514
%N Antidiagonal sums of triangle A124428.
%H G. C. Greubel, <a href="/A124429/b124429.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{k=0..[n/3]} C([(n-k)/2],k)*C([(n-k+1)/2],k)).
%t Table[Sum[Binomial[Floor[(n-k)/2], k]*Binomial[Floor[(n-k+1)/2], k], {k, 0, Floor[n/3]}], {n, 0, 40}] (* _G. C. Greubel_, Feb 24 2019 *)
%o (PARI) a(n)=sum(k=0,n\3,binomial((n-k)\2,k)*binomial((n-k+1)\2,k))
%o (Magma) [(&+[Binomial(Floor((n-k)/2), k)*Binomial(Floor((n-k+1)/2), k): k in [0..Floor(n/3)]]): n in [0..40]]; // _G. C. Greubel_, Feb 24 2019
%o (Sage) [sum(binomial(floor((n-k)/2),k)*binomial(floor((n-k+1)/2),k) for k in (0..floor(n/3))) for n in (0..40)] # _G. C. Greubel_, Feb 24 2019
%Y Cf. A124428, A124430.
%K nonn
%O 0,4
%A _Paul D. Hanna_, Oct 31 2006
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