Consider the recurrence relation \(a_n = 2a_{n-1} + 8a_{n-2}\text{,}\) with initial terms \(a_0 = 1\) and \(a_1= 3\text{.}\)

1. Find the next two terms of the sequence (\(a_2\) and \(a_3\)).

2. Solve the recurrence relation. That is, find a closed formula for the \(n\)th term of the sequence.