Sequences And Series

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 ______________.