ÖMO 2010 Problem 4

Consider the part of a lattice given by the corners $(0, 0), (n, 0), (n, 2)$ and $(0, 2)$ . From a lattice point $(a, b)$ one can move to $(a + 1, b)$ or to $(a + 1, b + 1)$ or to $(a, b - 1$ ), provided that the second point is also contained in the part of the lattice. How many ways are there to move from $(0, 0)$ to $(n, 2)$ considering these rules?