The recurrence $a_n = a_{n-1} - a_{n-2}$ with $a_0 = 1, a_1 = 0$ has complex characteristic roots $r = e^{\pm i\pi/3}$ (complex exponentials). Compute the sequence and determine its period (the smallest $p > 0$ such that $a_{n+p} = a_n$ for all $n \geq 0$).