Let $\left\{ a _ { n } \right\} _ { n = 1 } ^ { \infty }$ be a sequence such that $a _ { 1 } = 1 , a _ { 2 } = 1$ and $a _ { n + 2 } = 2 a _ { n + 1 } + a _ { n }$ for all $n \geq 1$. Then the value of $47 \sum _ { n = 1 } ^ { \infty } \left( \frac { a _ { n } } { 2 ^ { 3 n } } \right)$ is equal to $\underline{\hspace{1cm}}$.