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A086520 Number of integers strictly greater than (n-sqrt(n))/2 and strictly less than (n+sqrt(n))/2. 2

%I

%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="http://xxx.lanl.gov/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) inserted by _Alois P. Heinz_, Apr 02 2014

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Last modified October 24 16:24 EDT 2021. Contains 348233 sequences. (Running on oeis4.)