SE-SKOLORNAS 1980 Problem 5

A word is a string of the symbols $a, b$ which can be formed by repeated application of the following: (1) $ab$ is a word; (2) if $X$ and $Y$ are words, then so is $XY$ ; (3) if $X$ is a word, then so is $aXb$ . How many words have $12$ letters?