171 and 341. \(a_n = a_{n-1} + 2a_{n-2}\) with \(a_0 = 3\) and \(a_1 = 5\text{.}\) Closed formula: \(a_n = \frac{8}{3}2^n + \frac{1}{3}(-1)^n\text{.}\) To find this solve the characteristic equation, \(x^2 - x - 2 = 0\text{,}\) to get characteristic roots \(x = 2\) and \(x=-1\text{.}\) Then solve the system