Conditional variance of a Martingale Difference Sequence

Question

Suppose that $\{X_n\}$ is a martingale difference sequence adapted to $\{\mathcal{F}_n\}$. What are examples of $\{X_n\}$ such that $$ \sum_{i=1}^n\mathsf{E}[X_n^2\mid \mathcal{F}_{n-1}] $$ is constant? A trivial example is when $X_n$'s are independent, and $\mathcal{F}_n=\sigma(X_1,\ldots,X_n)$.