

A086520


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


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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


COMMENTS

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


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


EXAMPLE

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


MAPLE

a:= n> max(0, ceil((n+sqrt(n))/2)1floor((nsqrt(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]}]]


CROSSREFS

Sequence in context: A321861 A283431 A258594 * A012265 A268835 A006641
Adjacent sequences: A086517 A086518 A086519 * A086521 A086522 A086523


KEYWORD

easy,nonn


AUTHOR

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


EXTENSIONS

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


STATUS

approved



