The recurrence relation capturing the optimal execution time of the Towers of Hanoi problem with $n$ discs is

To solve the Towers of Hanoi problem with $n$ discs:

1. Move the top $n-1$ discs from the source peg to the auxiliary peg: takes $T(n-1)$ moves.

2. Move the largest disc from the source peg to the target peg: takes $1$ move.

3. Move the $n-1$ discs from the auxiliary peg to the target peg: takes $T(n-1)$ moves.

Summing these moves gives the total time:

with the base condition $T(1) = 1$.

Hence, the correct recurrence is D.