21.22 * Write an $n$-digit number using the digits 1 and 2, where no two adjacent digits are both 1, and let the number of such $n$-digit numbers be $f(n)$. Find $f(10)$.
It is known: $f(1)=2, f(2)=3, f(n+1)$ the number of $(n+1)$-digit numbers of this type can be divided into two categories: one ends with 2, there are $f(n)$ such numbers; the other ends with 1, the second last digit of this category must be 2, thus there are $f(n-1)$ such numbers, so $f(n+1)=f(n)+f(n-1)$, hence we can calculate $f(10)=144$.