2006 Fermat Problem 17

In seven term sequence, 5, p, q, 13, r, 40, x, each term after the third term is the sum of the preceding three terms. The value of x is

\textbf{(A)}\ 21\quad \textbf{(B)}\ 61\quad \textbf{(C)}\ 67\quad \textbf{(D)}\ 74\quad \textbf{(E)}\ 80

If there are no answer choices shown, enter a numerical answer.

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