2004 Pascal Problem 19

Rafaello's tree grows according to the following rule. After a branch has been growing for two weeks, it produces a new branch every week, while the original branch continues to grow. The tree has five branches after five weeks, as shown. How many branches, including the main branch, will the tree have at the end of eight weeks?

\textbf{(A)}\ 21\quad \textbf{(B)}\ 40\quad \textbf{(C)}\ 19\quad \textbf{(D)}\ 13\quad \textbf{(E)}\ 34

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

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