Sequence and Series: JEE Main 2021 Mathematics question

Let $\left\{ {{a_n}} \right\}_{n = 1}^\infty$ be a sequence such that a₁ = 1, a₂ = 1 and ${a_{n + 2}} = 2{a_{n + 1}} + {a_n}$ for all n $\ge$ 1. Then the value of $47\sum\limits_{n = 1}^\infty {{{{a_n}} \over {{2^{3n}}}}}$ is equal to ______________.