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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 31 2006
STATUS
approved