Cube painting

Consider the number of ways to paint the faces of a cube using n distinct colors. Let d(i) be i-th decimal digit of 41152/333333=0.123456123456... i.e. d(1)=1, d(5)=5, d(9)=3 etc. Let F(n) be the number of different cubes that can be obtained if it is allowed that upto d(i) faces can be painted with the i-th color. i=1,2,...,n. What is F(1001)? Example: 415 for F(5)