(9) Given the sequence $\left\{a_{n}\right\}$ satisfies $a_{1}=a_{2}=1, a_{n}=1-\frac{a_{1}+\cdots+a_{n-2}}{4}$ $(n \geqslant 3)$, find the general term formula for $a_{n}$.
$9 \begin{aligned} a_{n} & =1-\frac{a_{1}+\cdots+a_{n-2}}{4}=a_{n-1}-\frac{a_{n-2}}{4} \\ & \Rightarrow a_{n}-\frac{a_{n-1}}{2}=\frac{1}{2}\left(a_{n-1}-\frac{a_{n-2}}{2}\right)=\cdots=\frac{1}{2^{n-1}} \\ & \Rightarrow 2^{n-1} a_{n}=2^{n-2} a_{n-1}+1=\cdots=n \\ & \Rightarrow a_{n}=\frac{n}{2^{n-1}} .\end{aligned}$