Complex Numbers and Quadratic Equations: JEE Main 2021 Mathematics question

Let $\alpha$ and $\beta$ be two real numbers such that $\alpha$ + $\beta$ = 1 and $\alpha$$\beta$ = $-$1. Let p_n = ($\alpha$)^n + ($\beta$)^n, p_n$-$1 = 11 and p_n+1 = 29 for some integer n $\ge$ 1. Then, the value of p$_n^2$ is ___________.