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A129384 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, floor((n-k)/2)).

%I A129384 #8 Feb 03 2024 16:17:38
%S A129384 1,1,3,5,11,19,39,71,141,261,513,965,1889,3585,7017,13417,26287,50527,
%T A129384 99147,191399,376155,728619,1434051,2785667,5489823,10689199,21089799,
%U A129384 41146383,81262983,158818311,313935831,614469591,1215549981
%N A129384 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, floor((n-k)/2)).
%C A129384 Partial sums of A129383.
%H A129384 G. C. Greubel, <a href="/A129384/b129384.txt">Table of n, a(n) for n = 0..1000</a>
%F A129384 G.f.: (g(x) - x*g(x^2))/(1-x), where g(x) is the g.f. of A001405.
%F A129384 a(n) = Sum_{k=floor((n+1)/2)..n} binomial(k, floor(k/2)).
%t A129384 Table[Sum[Binomial[n-k,Floor[(n-k)/2]],{k,0,Floor[n/2]}],{n,0,40}] (* _Harvey P. Dale_, Aug 21 2021 *)
%o A129384 (Magma)
%o A129384 A129384:= func< n | (&+[Binomial(n-k, Floor((n-k)/2)): k in [0..Floor(n/2)]])  >;
%o A129384 [A129384(n): n in [0..40]]; // _G. C. Greubel_, Feb 03 2024
%o A129384 (SageMath)
%o A129384 def A129384(n): return sum(binomial(n-k,(n-k)//2) for k in range((n+2)//2))
%o A129384 [A129384(n) for n in range(41)] # _G. C. Greubel_, Feb 03 2024
%Y A129384 Cf. A001405, A129383.
%K A129384 easy,nonn
%O A129384 0,3
%A A129384 _Paul Barry_, Apr 12 2007