Question 32
Find the number of ordered $7$-tuples of positive integers $(a_1,a_2,a_3,a_4,a_5,a_6,a_7)$ that have both of the following properties:
(i) $a_n+a_{n+1}=a_{n+2}$ for $1\le n\le5$; and
(ii) $a_6=2005$.
(i) $a_n+a_{n+1}=a_{n+2}$ for $1\le n\le5$; and
(ii) $a_6=2005$.