11. The sequences $\left\{a_{n}\right\},\left\{b_{n}\right\}$ satisfy $a_{1}=2, b_{1}=1, a_{n+1}=5 a_{n}+3 b_{n}+7, b_{n+1}=3 a_{n}+5 b_{n}$ (where $n \in \mathbf{N}_{+}$), then the general term formula of $\left\{a_{n}\right\}$ is $a_{n}=$ $\qquad$ .
$$
\begin{array}{l}
\left\{\begin{array} { l } 
{ a _ { n + 1 } + b _ { n + 1 } = 8 ( a _ { n } + b _ { n } ) + 7 , } \\
{ a _ { n + 1 } - b _ { n + 1 } = 2 ( a _ { n } - b _ { n } ) + 7 }
\end{array} \Rightarrow \left\{\begin{array}{l}
a_{n+1}+b_{n+1}+1=8\left(a_{n}+b_{n}+1\right) \\
a_{n+1}-b_{n+1}+7=2\left(a_{n}-b_{n}+7\right)
\end{array}\right.\right. \\
\Rightarrow\left\{\begin{array}{l}
a_{n}+b_{n}=4 \cdot 8^{n-1}-1, \\
a_{n+1}-b_{n+1}=8 \cdot 2^{n-1}-7
\end{array} \Rightarrow a_{n}=2^{3 n-2}+2^{n+1}-4\left(n \in \mathbf{N}_{+}\right)\right.
\end{array}
$$