Let there be a matrix $$A_n=\left(\begin{matrix}4&2&\cdots&2\\2&4&\ddots&\vdots\\\vdots&\ddots&\ddots&2 \\2&\cdots&2&4\end{matrix}\right)\in M_n\left(\mathbb{Z}_7\right)$$
What is the general formula of $\det\left(A_n\right)$?
decomposition of the matrix to a sum will not help, any suggestions?