OFFSET
0,3
COMMENTS
Partial sums of A129383.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: (g(x) - x*g(x^2))/(1-x), where g(x) is the g.f. of A001405.
a(n) = Sum_{k=floor((n+1)/2)..n} binomial(k, floor(k/2)).
MATHEMATICA
Table[Sum[Binomial[n-k, Floor[(n-k)/2]], {k, 0, Floor[n/2]}], {n, 0, 40}] (* Harvey P. Dale, Aug 21 2021 *)
PROG
(Magma)
A129384:= func< n | (&+[Binomial(n-k, Floor((n-k)/2)): k in [0..Floor(n/2)]]) >;
[A129384(n): n in [0..40]]; // G. C. Greubel, Feb 03 2024
(SageMath)
def A129384(n): return sum(binomial(n-k, (n-k)//2) for k in range((n+2)//2))
[A129384(n) for n in range(41)] # G. C. Greubel, Feb 03 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 12 2007
STATUS
approved