Let $(X_n)_n$ be a stochastic process (with application regards $X_n$ as a distance between two points, hence those squares) with the next property
$\mathbb{E}(X_n^2 | X_{n-1}) = X_{n-1}^2 - X_{n-1} - 2$ and suppose $X_0$ is some (large enough) positive constant, so we do not have to deal with possibly negative values.
Is it true, that $\mathbb{E}(X_n | X_{n-1}) = X_{n-1} - \frac{1}{2}$ ?
Can something be said about $\mathbb{E}(X_n | X_{n-1})$ at all?