ÖMO 2003 Problem 5

We are given sufficiently many stones of the forms of a rectangle $2\times 1$ and square $1\times 1$ . Let $n > 3$ be a natural number. In how many ways can one tile a rectangle $3 \times n$ using these stones, so that no two $2 \times 1$ rectangles have a common point, and each of them has the longer side parallel to the shorter side of the big rectangle?