number of ways of constructing $n\times2$ rectangle from a $1\times2$ rectangle

Question

You are given $1\times2$ rectangles and you have to construct an $n\times2$ rectangle from it. Tell the number of ways of constructing $n\times2$ rectangle from a $1\times2$ rectangle

Answer 1

Hint: Let $a_n$ be the number of ways to construct the $2\times n$ rectanlge from $1\times 2$ rectangles. Then it is obvious that $a_1=1$ and $a_2 = 2$. Try to figure out what $a_{n}$ is with regard to $a_{n-2}$ and $a_{n-1}$. That is, find the reccurence relation to describe $a_n$.