VN-TST 1996 Problem 2

For each positive integer $n$ , let $f(n)$ be the maximal natural number such that: $2^{f(n)}$ divides $\sum^{\left\lfloor \frac{n - 1}{2}\right\rfloor}_{i=0} \binom{n}{2 \cdot i + 1} 3^i$ . Find all $n$ such that $f(n) = 1996.$