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

0,3

Links

Table of n, a(n) for n=0..39.

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}]

Prog

(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

Crossrefs

Cf. A068914.

Sequence in context: A002965 A206290 A091696 * A280303 A048808 A263358

Adjacent sequences: A334680 A334681 A334682 * A334684 A334685 A334686

Keyword

nonn

Author

Stefano Spezia, May 08 2020

Status

approved