Question 38
A sequence $(a_n)_{n \ge 1}$ is defined recursively as
$$
a_1 = 1, \ a_2 = 5, \text{ and } a_n = \frac{a_{n-1}^2 + 4}{a_{n-2}}, \text{ for } n \ge 3.
$$
Prove that every term in the sequence is an integer. Find an explicit formula for $a_n$.
$$
a_1 = 1, \ a_2 = 5, \text{ and } a_n = \frac{a_{n-1}^2 + 4}{a_{n-2}}, \text{ for } n \ge 3.
$$
Prove that every term in the sequence is an integer. Find an explicit formula for $a_n$.