A run of exactly three heads in six tosses

A fair coin is tossed six times. What is the probability that the sequence contains a block of exactly three heads in a row, i.e. three consecutive heads bordered on each side by a tail or by the end of the sequence?

$3/16$. The run can start at positions $1$–$4$. Starting at $1$ or $4$, one neighbour must be $T$ and the two other tosses are free ($4$ each); starting at $2$ or $3$, both neighbours are $T$ and one toss is free ($2$ each). That is $12$ of $64$ sequences.