AMC 8 2009 Problem 5

A sequence of numbers starts with $1$, $2$, and $3$. The fourth number of the sequence is the sum of the previous three numbers in the sequence: $1+2+3=6$. In the same way, every number after the fourth is the sum of the previous three numbers. What is the eighth number in the sequence? $\textbf{(A)}\ 11 \textbf{(B)}\ 20 \textbf{(C)}\ 37 \textbf{(D)}\ 68 \textbf{(E)}\ 99$