Let $$k_1, k_2, \ldots,$$ be a sequence that is recursively defined as $$k_{n+2} = k_{n+1} + 2 k_{n}$$, for all $$n\geq 1$$, with $$k_1 = k_2 = 1$$. The infinite sum, $$S = \frac{k_1}{7 ^1} + \frac{k_2}{7 ^2} + \frac{k_3}{7 ^3} \ldots$$, is a fraction of the form $$\frac{a}{b}$$, where $$a$$ and $$b$$ are coprime integers. What is the value of $$a+b$$?