The sequence of numbers 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, … is like the original Fibonacci sequence except that it is defined recursively by f1 = 1, f = 1, and fn+1 = fn + 2 for n >=2. The latter equation can be put into matrix form as

fn+1 1 2 fn
fn = 1 0 fn-1

By using the techniques (and showing the steps) that we did in class for the original Fibonacci sequence, find an explicit formula for f, in the sequence defined above. With that formula, use your calculator to find f22 and f50.