Question 160
Find out the number of sequences $(a_n)_{n=1}^{\infty}$ of integer numbers, which satisfy
$$
a_n \neq -1 \quad \text{and} \quad a_{n+2} = \frac{a_n + 2006}{a_{n+1} + 1}
$$
for every positive integer $n$.
$$
a_n \neq -1 \quad \text{and} \quad a_{n+2} = \frac{a_n + 2006}{a_{n+1} + 1}
$$
for every positive integer $n$.