已知数列\(\{a_{n}\}\)满足\(a_{1}=1\)，\(a_{n+1}=\begin{cases}{a_{n}+1,n\text{为奇数},}\\ {a_{n}+2,n\text{为偶数}.}\end{cases}\)
\((1)\)记\(b_{n}=a_{2n}\)，写出\(b_{1}\)，\(b_{2}\)，并求数列\(\{b_{n}\}\)的通项公式；
\((2)\)求\(\{a_{n}\}\)的前\(20\)项和.