# A Lucas Sum II

Calculus Level 4

Define the sequence $$\lbrace L_{n} \rbrace_{n=0}^{\infty}$$ by $$L_{0} = 2$$, $$L_{1} = 1$$, and $$L_{n+2} = L_{n+1}+L_{n}$$. If

$\sum_{n=0}^{\infty} \frac{L_{n}^{2}}{4^{n}}$

can be expressed in the form $$\frac{a}{b}$$ for positive coprime integers $$a$$ and $$b$$, find $$a+b$$.

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