## Nearly isosceles 120 degree triangles

### 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(10^{8})=1245.

Find T(10^{100}).