# Non-zero coefficients

**Discrete Mathematics**Level 5

Consider the polynomial

\[ f(x) = (x^{20} + x^{13} + 1)^{33}. \]

When fully expanded, how many terms have a non-zero coefficient?

**Details and assumptions**

As an explicit example, since \( (x^2 + 1)^3 = x^6 + 3x^4 + 3x^2 + 1 \), there are 4 terms with a non-zero coefficient.

You may use the fact that \( { 33 \choose 2 } = 528, {34 \choose 2 } = 561\) and \( { 35 \choose 2 } = 595 \).