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

Author

Paul D. Hanna, Oct 31 2006

Keywords

• nonn

Links

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

Crossrefs

Cf. A124428, A124430.

Programs

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

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 *)

PARI

a(n)=sum(k=0,n\3,binomial((n-k)\2,k)*binomial((n-k+1)\2,k))

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

Formula

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