A sequence is defined over non-negative integral indexes in the following way: $$a_{0}=a_{1}=3$$, $$a_{n+1}a_{n-1}=a_{n}^{2}+2007$$. Find the greatest integer that does not exceed $$\frac{a_{2006}^{2}+a_{2007}^{2}}{a_{2006}a_{2007}}$$

(第二十五届AIME1 2007 第14题)