KöMaL 2020 B5109

Let $x_1 = 2, x_2 = 7, x_{n+1} = 4 x_n - x_{n-1} (n=2,3,\ldots).$ Is there a perfect square in this sequence?

Official text KöMaL. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.