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Let $$\{a_n\}_{n=1}^\infty$$ be a sequence such that $$a_1 = 1$$, $$a_2 = 1$$ and $$a_{n+2} = 2a_{n+1} + a_n$$ for all $$n \ge 1$$. Then the value of $$47\sum_{n=1}^\infty \frac{a_n}{2^{3n}}$$ is equal to ___.
Correct Answer: 7
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