3 Let $a_{1}=a, a_{2}=b$; we successively compute $a_{3}=a+b ; \quad a_{4}=a+$ $2 b ; \quad \ldots ; \quad a_{10}=21 a+34 b$. The equation $2002=21 a+34 b$ has three positive integer solutions, namely $(84,7),(50,28),(16,49)$, and each of these gives a unique sequence.
Find the number of sequences $a_{1}, a_{2}, \ldots, a_{10}$ of positive integers with the property that $a_{n+2}=a_{n+1}+a_{n}$ for $n=1,2, \ldots, 8$, and $a_{10}=2002$.