ÖMO 2001 Problem 4

Let $A_o =\{1, 2\}$ and for $n> 0, A_n$ results from $A_{n-1}$ by adding the natural numbers to $A_{n-1}$ which can be represented as the sum of two different numbers from $A_{n-1}$ . Let $a_n = |A_n |$ be the number of numbers in $A_n$ . Determine $a_n$ as a function of $n$ .