Given the following matrix $M$, find an equation for $M^n$
$$M = \begin{pmatrix}0 & 1 & 0 & 0 \\ 0 & 0 & 1 &0 \\ 0 & 0& 0& 1 \\ 1& 0& 0& 0\end{pmatrix}$$
I’ve got as far as establishing that $n+1$ moves each $1$ entry a step to the right, but how do you translate this into an equation?
Notes :
\begin{align}M^2 &= \begin{pmatrix}0& 0& 1& 0 \\ 0& 0& 0& 1 \\ 1& 0& 0& 0 \\ 0& 1& 0& 0\end{pmatrix}\\ M^3 &= \begin{pmatrix}0& 0& 0& 1 \\ 1& 0& 0& 0 \\ 0& 1& 0& 0 \\ 0& 0& 1& 0\end{pmatrix}\\ M^4 &= \begin{pmatrix}1& 0& 0& 0 \\ 0& 1& 0& 0 \\ 0& 0& 1& 0 \\ 0& 0& 0& 1\end{pmatrix}\end{align}