A334683 Antidiagonal sums of A068914.

1, 1, 2, 3, 5, 7, 12, 17, 30, 44, 79, 120, 218, 341, 625, 1001, 1848, 3016, 5603, 9283, 17342, 29085, 54606, 92513, 174456, 298111, 564333, 971563, 1845364, 3198130, 6092038, 10621153, 20282471, 35554559, 68042537, 119874494, 229840130, 406794862, 781246800, 1388643835

Offset: 0

Author

Stefano Spezia, May 08 2020

Keywords

• nonn

Crossrefs

Cf. A068914.

Programs

Mathematica

T[n_,k_]:=Sum[(-1)^j*Binomial[n,Floor[(n+(k+2)j)/2]],{j,Floor[-n/(k+2)],Ceiling[n/(k+2)]}]; Table[Sum[T[n-k,k],{k,0,n}],{n,0,39}]

PARI

T(n,k) = sum(j=floor(-n/(k+2)), ceil(n/(k+2)), (-1)^j*binomial(n,floor((n+(k+2)*j)/2))); \\ A068914
a(n) = sum(k=0, n, T(n-k, k)); \\ Michel Marcus, May 09 2020