AMC 12 2015a Problem 22

For each positive integer $n$, let $S(n)$ be the number of sequences of length $n$ consisting solely of the letters $A$ and $B$, with no more than three $A$s in a row and no more than three $B$s in a row. What is the remainder when $S(2015)$ is divided by 12?

\textbf{(A)}\ 0 \textbf{(B)}\ 4 \textbf{(C)}\ 6 \textbf{(D)}\ 8 \textbf{(E)}\ 10