A124429 Antidiagonal sums of triangle A124428.

1, 1, 1, 2, 3, 5, 8, 13, 22, 36, 61, 102, 172, 292, 493, 841, 1429, 2439, 4169, 7124, 12216, 20930, 35940, 61749, 106155, 182749, 314638, 542338, 935195, 1613593, 2786037, 4811920, 8316435, 14378247, 24870062, 43036264, 74496224, 129008514

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..[n/3]} C([(n-k)/2],k)*C([(n-k+1)/2],k)).

Mathematica

Table[Sum[Binomial[Floor[(n-k)/2], k]*Binomial[Floor[(n-k+1)/2], k], {k, 0, Floor[n/3]}], {n, 0, 40}] (* G. C. Greubel, Feb 24 2019 *)

Prog

(PARI) a(n)=sum(k=0, n\3, binomial((n-k)\2, k)*binomial((n-k+1)\2, k))
(Magma) [(&+[Binomial(Floor((n-k)/2), k)*Binomial(Floor((n-k+1)/2), k): k in [0..Floor(n/3)]]): n in [0..40]]; // G. C. Greubel, Feb 24 2019
(Sage) [sum(binomial(floor((n-k)/2), k)*binomial(floor((n-k+1)/2), k) for k in (0..floor(n/3))) for n in (0..40)] # G. C. Greubel, Feb 24 2019

Crossrefs

Cf. A124428, A124430.

Sequence in context: A186085 A018151 A227374 * A306215 A018152 A293078

Adjacent sequences: A124426 A124427 A124428 * A124430 A124431 A124432

Keyword

nonn

Author

Paul D. Hanna, Oct 31 2006

Status

approved