$a_n^{(p)} = A \cdot 3^n$ (no resonance)

$a_n^{(p)} = An \cdot 3^n$ (resonance with simple root)

$a_n^{(p)} = An^2 \cdot 3^n$ (resonance with double root)

$a_n^{(p)} = A \cdot 3^n + B$