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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