Tower Of Hanoi (4 Pegs)

Question

In the Tower of Hanoi game, let $S_{n}$ denote the minimum number of moves needed to transfer $n$ disks from one tower to another tower when there are four towers.

1. Show that $Sm \leq 2$ · $Sm−k + 2^{k} − 1$, for $0 \leq k \leq m$.
2. Show that $S(n(n+1)/2) \leq 2^n*(n − 1) + 1$, for all $n \geq 0$.

Not sure what the equations meant, but I understand that the entire process takes $2S(k,r)+S(n-k,r-1)$ moves.