I'm trying to find the solution to the following recursion, but my attempts to inductively find it haven't been fruitful. Any ideas that may help?
$x_1 = a_1 + \dfrac{x_n}{4}+ \dfrac{x_2}{4}$
$x_2 = a_2 + \dfrac{x_1}{4}+ \dfrac{x_3}{4}$
$\vdots$
$x_{n-1} = a_{n-1} + \dfrac{x_{n-2}}{4}+ \dfrac{x_n}{4}$
$x_n = a_n + \dfrac{x_{n-1}}{4}+ \dfrac{x_1}{4}$