13. Let the sequence $\left\{a_{n}\right\}$ have the sum of the first $n$ terms $S_{n}=2 a_{n}-1(n=1,2, \cdots)$, and the sequence $\left\{b_{n}\right\}$ satisfies $b_{1}=3, b_{k+1}=a_{k}+b_{k}$ $(k=1,2,3, \cdots)$, find the sum of the first $n$ terms of the sequence $\left\{b_{n}\right\}$.