Induction · Hard problem

Let $f(n)$ be the number of subsets of $\{1, 2, \ldots, n\}$ with no two consecutive numbers. Break down by whether $n$ is in the subset to get $f(n) = f(n - 1) + f(n - 2)$, with $f(1) = 2$, $f(2) = 3$. What is $f(10)$?