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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