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

0,2

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.

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

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 *)

Prog

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

Crossrefs

Cf. A104684.

Sequence in context: A101850 A279002 A176280 * A045868 A171711 A363293

Adjacent sequences: A349710 A349711 A349712 * A349714 A349715 A349716

Keyword

nonn

Author

Michel Marcus, Nov 26 2021

Status

approved