Let <a_n > be a sequence such that a_0=0, a_1=1/2 and 2 a_n +2 =5 a_n +1 -3 a_n, n =0,1,2,3, …. Then Σ_k=1^100 a_k is equal to

Let $\displaystyle <a_{\mathrm{n}}>$ be a sequence such that $\displaystyle a_0=0, a_1=\frac{1}{2}$ and $\displaystyle 2 a_{\mathrm{n}+2}=5 a_{\mathrm{n}+1}-3 a_{\mathrm{n}}, \mathrm{n}=0,1,2,3, \ldots$. Then $\displaystyle \sum_{k=1}^{100} a_k$ is equal to