\left[
  \begin{array}{ c c c}
     x_{n+1}  \\
     x_{n} \\
     1
  \end{array} \right]
=
\left[
  \begin{array}{ c c c}
     34 & -1 & -4  \\
     1 & 0 & 0 \\
     0 & 0 & 1
  \end{array} \right]^n
\left[
  \begin{array}{ c c c}
     2  \\
     2 \\
     1
  \end{array} \right]