C_n= \left|
  \begin{array}{ c c c c c c c c c c }
  x-2 & 1 & 0 & 0 & 0 & \cdots & 0 & 0 & 0\\
  1 & x-2 & 1 & 0 & 0 & \cdots & 0 & 0 & 0\\
  0 & 1 & x-2 & 1 & 0 & \cdots & 0 & 0 & 0\\
  0 & 0 & 1 & x-2 & 1 & \cdots & 0 & 0 & 0 \\
  0 & 0 & 0 & 1 & x-2 & \cdots & 0 & 0 & 0 \\
  \vdots & & & & \vdots & & \vdots & & \vdots \\
  0 & 0 & 0 & 0 & 0 & \cdots & 1 & x-2 & 1\\
  0 & 0 & 0 & 0 & 0 & \cdots & 0 & 1 & x-2\\
\end{array} \right|