8. Invent your own recursively defined sequence $a_n$, but make sure it satisfies the following properties:
• $a_n$ must depend on the three previous terms $a_{n-1}$, $a_{n-2}$ and $a_{n-3}$.
• You must use the initial conditions $a_0 = 1$, $a_1 = -1$, and $a_2 = 1/2$
Calculate the term $a_8$.
