A run of exactly three heads in six tosses

Toss a fair coin $6$ times. What is the probability that the sequence contains a block of exactly three heads in a row (a maximal run of length $3$, not part of a longer run)?

$3/16$. The run can start in position $1,2,3$ or $4$. A run at an end needs a tail beside it and leaves two free tosses ($4$ sequences each); a run in the middle needs tails on both sides and leaves one free toss ($2$ each). That gives $2(4+2)=12$ of $64$ sequences, i.e. $\tfrac{3}{16}$.