The recurrence $a_n = -a_{n-2}$ with $a_0 = 1, a_1 = 0$ has characteristic roots $r = \pm i$ (purely imaginary). These can be written as $r = e^{\pm i\pi/2}$. What is the period of the sequence (smallest positive $p$ such that $a_{n+p} = a_n$ for all $n$)?