$a_n = c_1(2+i)^n + c_2(2-i)^n$

$a_n = (\sqrt{5})^n (c_1 \cos(n\theta) + c_2 \sin(n\theta))$ where $\tan \theta = 0.5$

$a_n = c_1 2^n \cos(n) + c_2 2^n \sin(n)$

$a_n = c_1(2)^n + c_2(i)^n$