The sequence \left(a_{n}\right) satisfies a_{0}=0 and a_{n+1}=\frac{8}{5} a_{n}+\frac{6}{5} \sqrt{4^{n}-a_{n}^{2}} for n \geq 0. Find the greatest integer less than or equal to a_{10}.
The sequence \left(a_{n}\right) satisfies a_{0}=0 and a_{n+1}=\frac{8}{5} a_{n}+\frac{6}{5} \sqrt{4^{n}-a_{n}^{2}} for n \geq 0. Find the greatest integer less than or equal to a_{10}.