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

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, 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, 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

Offset: 0

Author

Jeff S. Pratt (jpratt(AT)pas.rochester.edu), Sep 10 2003

Keywords

• easy
• nonn

Comments

This sequence occurs in quantum mechanics, in the context of counting certain kinds of inseparable states in an n-qubit model.

Examples

			a(16) = 3 because there are three integers between 6 and 10.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• J. S. Pratt, Universality in the entanglement structure of ferromagnets, Phys. Rev. Lett. 93, 237205 (2004)
• J. S. Pratt, Comments on this sequence

Programs

Maple

a:= n-> max(0, ceil((n+sqrt(n))/2)-1-floor((n-sqrt(n))/2)):
seq(a(n), n=0..120);  # Alois P. Heinz, Apr 02 2014

Mathematica

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]}]]

Extensions

a(0)-a(1) prepended by Alois P. Heinz, Apr 02 2014