AIME 2002a Problem 8

Find the smallest integer $k$ for which the conditions (1) $a_1,a_2,a_3\cdots$ is a nondecreasing sequence of positive integers (2) $a_n=a_{n-1}+a_{n-2}$ for all $n>2$ (3) $a_9=k$ are satisfied by more than one sequence.