This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A086520 #15 Jan 27 2022 09:20:56
%S A086520 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 A086520 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 A086520 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 A086520 Number of integers strictly greater than (n-sqrt(n))/2 and strictly less than (n+sqrt(n))/2.
%C A086520 This sequence occurs in quantum mechanics, in the context of counting certain kinds of inseparable states in an n-qubit model.
%H A086520 Alois P. Heinz, <a href="/A086520/b086520.txt">Table of n, a(n) for n = 0..1000</a>
%H A086520 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 A086520 J. S. Pratt, <a href="/A086520/a086520.txt">Comments on this sequence</a>
%e A086520 a(16) = 3 because there are three integers between 6 and 10.
%p A086520 a:= n-> max(0, ceil((n+sqrt(n))/2)-1-floor((n-sqrt(n))/2)):
%p A086520 seq(a(n), n=0..120); # _Alois P. Heinz_, Apr 02 2014
%t A086520 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 A086520 easy,nonn
%O A086520 0,4
%A A086520 Jeff S. Pratt (jpratt(AT)pas.rochester.edu), Sep 10 2003
%E A086520 a(0)-a(1) prepended by _Alois P. Heinz_, Apr 02 2014