1. [12 pts] (Recurrence) For $n \ge 1$, let $a_n$ be the number of ways to completely cover a $2 \times n$ board with $1 \times 2$ blocks called dominoes, where each domino can be either yellow or white. Find a recurrence relation, along with the necessary initial conditions, for the sequence formed by $a_n$. (Observe that each domino can be placed horizontally or vertically.)