# Recursion in between

Algebra Level pending

$\large{{ a }_{ n+1 }=\left\lfloor \frac { 4 }{ 3 } \left( \left\lfloor \sqrt { { a }_{ n }^{ 2 }+5{ a }_{ n } } \right\rfloor \right) \right\rfloor }$

Let there be a sequence defined by above rule for $$n\ge 1$$. If $$a_{16}=628$$ and the first perfect square immediately before $$a_{16}$$ occurs at $$a_{x}$$ ($$x<14$$) and $$\large{\left\lfloor \frac { { a }_{ 20 } }{ { a }_{ 10 } } \right\rfloor =y}$$. Find $$x+y$$

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