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%I #15 Jan 27 2022 09:20:56
%S 0,0,1,2,1,2,3,2,3,2,3,4,3,4,3,4,3,4,5,4,5,4,5,4,5,4,5,6,5,6,5,6,5,6,
%T 5,6,5,6,7,6,7,6,7,6,7,6,7,6,7,6,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,9,8,
%U 9,8,9,8,9,8,9,8,9,8,9,8,9,8,9,10,9,10,9,10,9,10,9,10,9,10,9,10,9,10,9,10,9,10
%N Number of integers strictly greater than (n-sqrt(n))/2 and strictly less than (n+sqrt(n))/2.
%C This sequence occurs in quantum mechanics, in the context of counting certain kinds of inseparable states in an n-qubit model.
%H Alois P. Heinz, <a href="/A086520/b086520.txt">Table of n, a(n) for n = 0..1000</a>
%H J. S. Pratt, <a href="https://arxiv.org/abs/quant-ph/0411125">Universality in the entanglement structure of ferromagnets</a>, Phys. Rev. Lett. 93, 237205 (2004)
%H J. S. Pratt, <a href="/A086520/a086520.txt">Comments on this sequence</a>
%e a(16) = 3 because there are three integers between 6 and 10.
%p a:= n-> max(0, ceil((n+sqrt(n))/2)-1-floor((n-sqrt(n))/2)):
%p seq(a(n), n=0..120); # _Alois P. Heinz_, Apr 02 2014
%t a[n_] := If[IntegerQ[Sqrt[n]], Sum[1, {m, Ceiling[(n - Sqrt[n])/2] + 1, Floor[(n + Sqrt[n])/2] - 1}], Sum[1, {m, Ceiling[(n - Sqrt[n])/2], Floor[(n + Sqrt[n])/2]}]]
%K easy,nonn
%O 0,4
%A Jeff S. Pratt (jpratt(AT)pas.rochester.edu), Sep 10 2003
%E a(0)-a(1) prepended by _Alois P. Heinz_, Apr 02 2014
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