Hints:
Let $a_n$ be the number of words of length $n$ which do not end with a B and $b_n$ be the number of words which do end with a B. So the total number of words of length $n$ is $a_n+b_n$.
Can you see the starting position is $a_0=1$ and $b_0=0$?
Can you express $a_n$ and $b_n$ in terms of $a_{n-1}$ and $b_{n-1}$?
Can you then express $a_n$ in terms of $a_{n-1}$ and $a_{n-2}$?
Can you solve this recurrence to find an expression for $a_n$ in terms of $n$?
Can you find expressions for $b_n$ and for $a_n+b_n$?