Coefficients of a particular polynomial

Question

Let $f$ be the polynomial obtained by taking the terms $1$, $x^3$, $x^6$, $x^9$, ... $x^k$,... for $k\equiv 0,3,6$ (mod 9) in the expansion of $(1+x)^n$ with the corresponding coefficients. That is, $$f(x) = \sum_{k\leq n, k \equiv 0,3,6} \binom{n}{k} x^k$$ What are the (complex) roots of $f$?