The Lucas sequence is defined by the recurrence $L_n = L_{n-1} + L_{n-2}$ with initial conditions $L_0 = 2$ and $L_1 = 1$. (Note: This differs from Fibonacci.) If the Fibonacci sequence is $F_n = \frac{\phi^n - \psi^n}{\sqrt{5}}$ where $\phi = \frac{1+\sqrt{5}}{2}$ and $\psi = \frac{1-\sqrt{5}}{2}$, which is the closed form for $L_n$?