$a_n = c_1 \cdot 2^n + c_2 \cdot 3^n$

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

$a_n = c_1 \cdot 4^n + c_2$

$a_n = c_1 \cdot 2^n + c_2 \cdot n^2$