JEE Math Practice Question

Let $$\{ {a_n}\} _{n = 0}^\infty $$ be a sequence such that $${a_0} = {a_1} = 0$$ and $${a_{n + 2}} = 2{a_{n + 1}} - {a_n} + 1$$ for all n $$\ge$$ 0. Then, $$\sum\limits_{n = 2}^\infty {{{{a_n}} \over {{7^n}}}} $$ is equal to:

1. A.$${6 \over {343}}$$
2. B.$${7 \over {216}}$$
3. C.$${8 \over {343}}$$
4. D.$${{49} \over {216}}$$