Question 70
We wish to color the squares in a strip of $n$ squares that are numbered from $1$ through $n$ from left to right. Each square is to be colored with one of the colors $1$, $2$ or $3$. The even numbered squares can be colored with any color, but the odd numbered squares can only be colored with the odd colors $1$ or $3$. In how many ways can the strip be colored if no two adjoining squares may have the same color?