I have the 7 following reccurence relations:
$A_n = B_{n-1} + C_{n-1}$
$B_n = A_n + C_{n-1}$
$C_n = B_n + C_{n-1}$
$D_n = E_{n-1} + G_{n-1}$
$E_n = D_n + F_{n-1}$
$F_n = G_n + C_n$
$G_n = E_n + F_{n-1}$
which I would like to solve, with the goal of eventually finding an explicit form of $E_n$. I started out by looking at only $A_n$, $B_n$ and $C_n$, and found a formula for $A_n$.
$A_n = 1/3 \sqrt{3} (2+ \sqrt{3})^n - 1/3 \sqrt{3} (2 - \sqrt{3})^n$
but I cant seem to find the right trick this time.