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

%I A095719 #10 Oct 21 2024 04:31:15
%S A095719 1,1,2,2,4,5,8,11,18,25,40,59,90,137,210,319,492,754,1164,1798,2786,
%T A095719 4317,6710,10438,16266,25377,39650,62013,97108,152212,238822,375058,
%U A095719 589520,927365,1459960,2300097,3626211,5720649,9030450,14263675
%N A095719 a(n) = Sum_{k = 0..floor(n/2)} floor(C(n-k,k)/(k+1)).
%C A095719 Sums of diagonal entries in A011847.
%H A095719 G. C. Greubel, <a href="/A095719/b095719.txt">Table of n, a(n) for n = 1..1000</a>
%F A095719 a(n) = Sum_{k=0..floor(n/2)} floor(C(n-k,k)/(k+1)).
%p A095719 a:=n->add(floor(C(n-k,k)/(k+1)),k=0..n/2);
%t A095719 Table[Sum[Floor[Binomial[n-k,k]/(k+1)],{k,0,n/2}],{n,40}] (* _Harvey P. Dale_, Apr 02 2019 *)
%o A095719 (Magma)
%o A095719 A095719:= func< n | (&+[Floor(Binomial(n-k,k)/(k+1)): k in [0..Floor(n/2)]]) >;
%o A095719 [A095719(n): n in [1..40]]; // _G. C. Greubel_, Oct 21 2024
%o A095719 (SageMath)
%o A095719 def A095719(n): return sum(binomial(n-k,k)//(k+1) for k in range(n//2+1))
%o A095719 [A095719(n) for n in range(1,41)] # _G. C. Greubel_, Oct 21 2024
%Y A095719 Cf. A011847, A095718.
%K A095719 nonn
%O A095719 1,3
%A A095719 _Mike Zabrocki_, Jul 08 2004