2009 AMC 8 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\qquad\textbf{(B)}\ 20\qquad\textbf{(C)}\ 37\qquad\textbf{(D)}\ 68\qquad\textbf{(E)}\ 99

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.