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\left(\begin{array}{cc}x_{n+1}\\y_{n+1}\end{array}\right)=\begin{array}{cc}A\end{array}\left(\begin{array}{cc}x_n\\y_n\end{array}\right)=\begin{array}{cc}A^n\end{array}\left(\begin{array}{cc}x_1\\y_1\end{array}\right)
S_n-S_{n-1}=a_n
S_n=n^2
\sum_{k=1}^n{c}=cn
a_{n+2}=a_{n+1}+a_n,a_1=a_0=1