A129384 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, floor((n-k)/2)).
1, 1, 3, 5, 11, 19, 39, 71, 141, 261, 513, 965, 1889, 3585, 7017, 13417, 26287, 50527, 99147, 191399, 376155, 728619, 1434051, 2785667, 5489823, 10689199, 21089799, 41146383, 81262983, 158818311, 313935831, 614469591, 1215549981
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Programs
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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
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Mathematica
Table[Sum[Binomial[n-k,Floor[(n-k)/2]],{k,0,Floor[n/2]}],{n,0,40}] (* Harvey P. Dale, Aug 21 2021 *) -
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
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)).
Comments