Imagine an infinite sequence of coin tosses, each yielding $h$ or $t.$
If the $n\text{th,}$ $(n+1)\text{th},$ and $(n+2)\text{th}$ tosses yield (for example) $hth,$ then the $(n+1)\text{th},$ $(n+2)\text{th},$ and $(n+3)\text{th}$ tosses may be either $thh$ or $tht.$ Thus the set of all eight sequences of length $3$ is a Markov chain whose directed graph looks like this: $$ \begin{array}{ccccccccccccccc} & & & hht & & & \longrightarrow & & & htt \\ & & \nearrow & & \searrow & & & & \nearrow & & \searrow \\ \hookrightarrow & hhh & & \uparrow & & hth & \longleftrightarrow & tht & & \downarrow & & ttt & \hookleftarrow \\ & & \nwarrow & & \swarrow & & & & \nwarrow & &\swarrow \\ & & & thh & & & \longleftarrow & & & tth \end{array} $$ I've attempted to make a neat and orderly and graphically legible and pleasing version of the corresponding graph for four consecutive tosses and I can see as the number increases this may become challenging. Is this a solved problem? If so, is the solution in print somewhere? And can it be described here?