Let { a_n }_n =0^∞ be a sequence such that a_0= a_1=0 and a_n +2 =2 a_n +1 - a_n +1 for all n ≥ 0. Then, Σ_n =2^∞ (a_n)/(7^n) is equal to:

Let $\displaystyle \left\{\mathrm{a}_{\mathrm{n}}\right\}_{\mathrm{n}=0}^{\infty}$ be a sequence such that $\displaystyle \mathrm{a}_0=\mathrm{a}_1=0$ and $\displaystyle \mathrm{a}_{\mathrm{n}+2}=2 \mathrm{a}_{\mathrm{n}+1}-\mathrm{a}_{\mathrm{n}}+1$ for all $\displaystyle \mathrm{n} \geqslant 0$. Then, $\displaystyle \sum_{\mathrm{n}=2}^{\infty} \frac{\mathrm{a}_{\mathrm{n}}}{7^{\mathrm{n}}}$ is equal to :