2011 Pascal Problem 13

The first four terms of a sequence are 1, 4, 2, and 3. Beginning with the fifth term in the sequence, each term is the sum of the previous four terms. Therefore, the fifth term is 10. What is the eighth term?

\textbf{(A)}\ 66\quad \textbf{(B)}\ 65\quad \textbf{(C)}\ 69\quad \textbf{(D)}\ 134\quad \textbf{(E)}\ 129

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Full credit to this problem is given to the CEMC, you may view all Pascal contests here.