The Lucas numbers satisfy the recurrence relation
L_n = L_(n−1) + L_(n−2), and the initial conditions L_0 = 2 and L_1 = 1.
a) Show that L_n = f_(n−1) +f_(n+1) for n = 2,3,..., where f_n is the nth Fibonacci number.
b) Find an explicit formula for the Lucas numbers.
