  In the Tower of Hanoi problem, there is six types of moves between the three
pegs. The main purpose of the present paper is to find out the number of each
of these six elementary moves in the optimal sequence of moves. We present a
recursive function based on indicator functions, which counts the number of
each elementary move, we investigate some of its properties including
combinatorial identities, recursive formulas and generating functions. Also we
found and interesting sequence that is strongly related to counting each type
of these elementary moves that we'll establish some if its properties as well.
