A095719 a(n) = Sum_{k = 0..floor(n/2)} floor(C(n-k,k)/(k+1)).

1, 1, 2, 2, 4, 5, 8, 11, 18, 25, 40, 59, 90, 137, 210, 319, 492, 754, 1164, 1798, 2786, 4317, 6710, 10438, 16266, 25377, 39650, 62013, 97108, 152212, 238822, 375058, 589520, 927365, 1459960, 2300097, 3626211, 5720649, 9030450, 14263675

Offset: 1

Author

Mike Zabrocki, Jul 08 2004

Keywords

• nonn

Comments

Sums of diagonal entries in A011847.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A011847, A095718.

Programs

Magma

A095719:= func< n | (&+[Floor(Binomial(n-k,k)/(k+1)): k in [0..Floor(n/2)]]) >;
[A095719(n): n in [1..40]]; // G. C. Greubel, Oct 21 2024

Maple

a:=n->add(floor(C(n-k,k)/(k+1)),k=0..n/2);

Mathematica

Table[Sum[Floor[Binomial[n-k,k]/(k+1)],{k,0,n/2}],{n,40}] (* Harvey P. Dale, Apr 02 2019 *)

SageMath

def A095719(n): return sum(binomial(n-k,k)//(k+1) for k in range(n//2+1))
[A095719(n) for n in range(1,41)] # G. C. Greubel, Oct 21 2024

Formula

a(n) = Sum_{k=0..floor(n/2)} floor(C(n-k,k)/(k+1)).