Nearly isosceles 120 degree triangles

Published on Sunday, 18th December 2016, 10:00 am; Solved by 235;
Difficulty rating: 50%

Problem 582

Let a, b and c be the sides of an integer sided triangle with one angle of 120 degrees, a≤b≤c and b-a≤100.
Let T(n) be the number of such triangles with c≤n.
T(1000)=235 and T(108)=1245.
Find T(10100).