AT-OEMO-FED1 2012 Problem 3

Consider a stripe of $n$ fieds, numbered from left to right with the integers $1$ to $n$ in ascending order. Each of the fields is colored with one of the colors $1$ , $2$ or $3$ . Even-numbered fields can be colored with any color. Odd-numbered fields are only allowed to be colored with the odd colors $1$ and $3$ . How many such colorings are there such that any two neighboring fields have different colors?