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)