Find the smallest integer k for which the conditions (1) $$a_1, a_2, a_3, \ldots$$ 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.

(第二十届AIME1 2002 第8题)