已知数列\(\{a_{n}\}\)满足\(a_{1}=1\)，\(a_{n+1}=\begin{cases}{2a_{n},n\text{为奇数}}\\ {a_{n}+3,n\text{为偶数}}\end{cases}.\)
\((1)\)从下面两个条件中选一个，写出\(b_{1}\)，\(b_{2}\)，并求数列\(\{b_{n}\}\)的通项公式；
①\(b_{n}=a_{2n-1}+3\)；
②\(b_{n}=a_{2n+1}-a_{2n-1}.\)
\((2)\)求数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}.\)