A010757 Sum along upward diagonal of Pascal triangle from center.

1, 0, 1, 2, 1, 3, 7, 4, 11, 25, 16, 41, 92, 63, 155, 344, 247, 591, 1300, 967, 2267, 4950, 3785, 8735, 18955, 14820, 33775, 72905, 58060, 130965, 281403, 227612, 509015, 1089343, 892926, 1982269, 4227273, 3505386, 7732659, 16438345, 13770404, 30208749, 64037453

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) = A010756(n) + A000984(n/3) if 3|n, otherwise a(n) = A010756(n). - R. J. Mathar, Feb 08 2016

Maple

seq(add(binomial(i-k, k), k=ceil(i/3)..floor(i/2)), i=0..50); # Detlef Pauly (dettodet(AT)yahoo.de), Jul 24 2003

Prog

(PARI) a(n) = sum(k=(n+2)\3, n\2, binomial(n-k, k)); \\ Seiichi Manyama, Feb 10 2022

Crossrefs

Cf. A000045, A000984, A007318, A010752, A010753, A010756.

Sequence in context: A058170 A238206 A127896 * A323943 A286616 A019320

Adjacent sequences: A010754 A010755 A010756 * A010758 A010759 A010760

Keyword

nonn

Author

R. K. Guy

Status

approved