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A124429
Antidiagonal sums of triangle A124428.
3
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
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
Sequence in context: A186085 A018151 A227374 * A306215 A018152 A293078
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 31 2006
STATUS
approved