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A349713 Antidiagonal sums of triangle A104684.

%I A349713 #20 Apr 23 2025 04:49:53
%S A349713 1,2,7,26,101,404,1645,6784,28243,118442,499601,2117366,9008969,
%T A349713 38458644,164643197,706574780,3038800419,13093784762,56513880913,
%U A349713 244283771986,1057348164103,4582148496448,19879232544027,86331108851932,375262802895691,1632570339730086,7108008200622949
%N A349713 Antidiagonal sums of triangle A104684.
%C A349713 Diagonal of the rational function 1 / (1 - x - y - (x*y)^2). - _Ilya Gutkovskiy_, Apr 22 2025
%H A349713 Michel Marcus, <a href="/A349713/b349713.txt">Table of n, a(n) for n = 0..1000</a>
%H A349713 Ömür Deveci and Anthony G. Shannon, <a href="http://www.montis.pmf.ac.me/vol50/4.pdf">Some aspects of Neyman triangles and Delannoy arrays</a>, Mathematica Montisnigri, Volume L, 2021.
%F A349713 a(n) = Sum_{k=0..floor(n/2)} A104684(n-k, k).
%F A349713 G.f.: 1/sqrt(x^4-2*x^2-4*x+1). - _Alois P. Heinz_, Nov 26 2021
%t A349713 nterms=30;Table[Sum[Binomial[r=n-k,k]Binomial[2r-k,r],{k,0,Floor[n/2]}],{n,0,nterms-1}] (* _Paolo Xausa_, Nov 26 2021 *)
%o A349713 (PARI) T(n, k) = binomial(n, k)*binomial(2*n-k, n); \\ A104684
%o A349713 a(n) = sum(k=0, n\2, T(n-k, k));
%Y A349713 Cf. A104684.
%K A349713 nonn
%O A349713 0,2
%A A349713 _Michel Marcus_, Nov 26 2021