==== Recurrent Problems - The Tower of Hanoi ====
T<sub>n</sub> is the minimum number of moves that will transfer n disks from one peg to another under Lucas's rules.

===== small cases =====
T<sub>0</sub> = 0,  T<sub>1</sub> = 1,  T<sub>2</sub> = 3 .....

===== mathematical expression ===== 
'''T<sub>0</sub> = 0,   T<sub>n</sub> = 2T<sub>n - 1</sub> + 1, for n > 0'''

===== closed form =====
'''T<sub>n</sub> = 2<sup>n</sup> - 1, for n >= 0'''