Question 1
Consider the sequence $a_1, a_2, a_3, \dots$ defined by $a_1 = 9$ and
$$
a_{n+1} = \frac{(n+5)a_n + 22}{n+3}
$$
for $n \ge 1$. Find all positive integers $n$ for which $a_n$ is a perfect square.
$$
a_{n+1} = \frac{(n+5)a_n + 22}{n+3}
$$
for $n \ge 1$. Find all positive integers $n$ for which $a_n$ is a perfect square.