OFFSET
0,2
COMMENTS
Partial sums of A129369.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: (1/(1-x))*( 1/sqrt(1-4*x) - x/sqrt(1-4*x^2) ).
a(n) = Sum_{k=0..floor(n/2)} C(2*(n-k), n-k).
MATHEMATICA
Table[Sum[Binomial[2k, k], {k, Floor[(n+1)/2], n}], {n, 0, 30}] (* Harvey P. Dale, Aug 13 2012 *)
PROG
(Magma) [(&+[Binomial(2*(n-k), n-k): k in [0..Floor(n/2)]]): n in [0..60]]; // G. C. Greubel, Jan 31 2024
(SageMath) [sum(binomial(2*(n-k), n-k) for k in range(1+(n//2))) for n in range(61)] # G. C. Greubel, Jan 31 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 11 2007
STATUS
approved