# Magical sequence

Algebra Level 5

The sequence $$(a_n)$$ satisfies $$a_0=0$$ and $$a_{n + 1} = \dfrac85a_n + \dfrac65\sqrt {4^n - a_n^2}$$ for $$n\geq 0$$ . Find $$\lfloor{(a_{10})}\rfloor$$

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