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

0,3

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

Cf. A001405, A129383.

Sequence in context: A320795 A285230 A089098 * A131887 A045691 A045961

Adjacent sequences: A129381 A129382 A129383 * A129385 A129386 A129387

Keyword

easy,nonn

Author

Paul Barry, Apr 12 2007

Status

approved