DYNAMIC PROGRAMMING: 

Find the number of ways N(m) in which one can move from 0 to m>0 (points located on a real line). Each path should satisfy several rules: 1) only non-zero integer steps are allowed 2) steps should always be to the right (backing up is not allowed) 3) last step should land on m (overshooting is not allowed). Solution should contain a formula expressing N(m) in terms of N(k) with k