A349713 Antidiagonal sums of triangle A104684.

1, 2, 7, 26, 101, 404, 1645, 6784, 28243, 118442, 499601, 2117366, 9008969, 38458644, 164643197, 706574780, 3038800419, 13093784762, 56513880913, 244283771986, 1057348164103, 4582148496448, 19879232544027, 86331108851932, 375262802895691, 1632570339730086, 7108008200622949

Offset: 0

Author

Michel Marcus, Nov 26 2021

Keywords

• nonn

Comments

Diagonal of the rational function 1 / (1 - x - y - (x*y)^2). - Ilya Gutkovskiy, Apr 22 2025

Links

• Michel Marcus, Table of n, a(n) for n = 0..1000
• Ömür Deveci and Anthony G. Shannon, Some aspects of Neyman triangles and Delannoy arrays, Mathematica Montisnigri, Volume L, 2021.

Crossrefs

Cf. A104684.

Programs

Mathematica

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 *)

PARI

T(n, k) = binomial(n, k)*binomial(2*n-k, n); \\ A104684
a(n) = sum(k=0, n\2, T(n-k, k));

Formula

a(n) = Sum_{k=0..floor(n/2)} A104684(n-k, k).

G.f.: 1/sqrt(x^4-2*x^2-4*x+1). - Alois P. Heinz, Nov 26 2021