Number of solutions by generating functions

Question

**Q4 Find the number of ordered triples $(x, y, z)$ of nonnegative integers satisfying the conditions:

(i) x ≤ y ≤ z;

(ii) x + y + z ≤ 100. (RMO 2003 INDIA)**

My approach to the problem is through generating function.

Let y = x + a and z = y + b

Hence 3x + 2a + b + c = 100

Hence number of solution is

[x^100] in { (1-x^3)(1-x^2)(1-x)^2 }^-1

I am not able to find it

Answer 1

Using Wolframalpha, I get 30,787:

Wolframalpha

I used the SeriesCoefficient function in Wolframalpha.