I believe this is a simple problem but im not sure if im satisfied with my solution.
We are tossing a fair coin. Let $X_n$ be the number of heads thrown in the $n+1$ and $n+2$ throw. Does the sequence $X_1, X_2, X_3, \dots$ form a Markov chain.
My solution is a simple observation that $X_n$ does not satisfy the Markov property, wich means that when we are in state $n$ we have to know the states $n +1 $ and $n + 2$ in order to determine $X_n$.
Is my reasoning correct? How could I argue rigorously that $X_1, X_2, X_3, \dots$ does not form a Markov chain?