Recursive Formulas - Definition & Examples

Define a sequence $\{a_n\}$ such that $a_1=a_2 = 1, a_3 = 2$ and

$$a_n + a_{n-3} = a_{n-1} + a_{n-2}$$

for $n > 3$. What is the value of $a_7$?

Source: Lexington Math Tournament