This is a project for Alias to practice the programming with Math.
Use the Matrix Formula to sove this Problem. $$ \left( \begin{matrix} -2 & 1 & 2 \ -1 & 2 & 2 \ -2 & 2 & 3 \end{matrix} \right)^k \left( \begin{matrix} 3 \ 4 \ 5 \end{matrix} \right) $$
MIT License