CR-MO 2018 F2

Consider $f (n, m)$ the number of finite sequences of $1$ 's and $0$ 's such that each sequence that starts at $0$ , has exactly n $0$ 's and $m$ $1$ 's, and there are not three consecutive $0$ 's or three $1$ 's. Show that if $m, n> 1$ , then $$f (n, m) = f (n-1, m-1) + f (n-1, m-2) + f (n-2, m-1) + f (n-2, m-2)$$