# Non-zero coefficients

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 $${ 35 \choose 2 } = 595$$.

×