Two solutions to a homogeneous recurrence are $\phi_n^{(1)} = 2^n$ and $\phi_n^{(2)} = n \cdot 3^n$. Compute their Casoratian (discrete Wronskian): $W_n = \phi_n^{(1)} \phi_{n+1}^{(2)} - \phi_n^{(2)} \phi_{n+1}^{(1)}$