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　2次元列ベクトル$A_n$ $(n=1,2,3,\cdots)$が
\[ A_1=\begin{pmatrix} 2 \\ 1 \end{pmatrix}, \hspace{1zw}
A_2=\begin{pmatrix} 3 \\ 1 \end{pmatrix}, \hspace{1zw}
A_{n+2}=\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}A_{n+1}+\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}A_n
\hspace{1zw} (n=1,2,3,\cdots) \]
を満たすとき，$A_n$を求めよ．
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