Jumping stairs

There is a stair with N step. You can jump either 1 step or 2 steps at time. How many different ways do you want to reach the top?

Solution

N = 1 --> 1
N = 2 ,,  1s+1s, 2s -> 2
N = 3 , 1s+1s+1s, 2s+1s, 1s+2s -> 3
N = 4, 1s+1s+1s+1s, 1s+1s+2s, 1s+2s+1s, 2s+1s+1s, 2s+2s -> 5
N = 5, 1s+1s+1s+1s+1s, 1s+1s+1s+2s, 1s+1s+2s+1s, 1s+2s+1s+1s, 2s+1s+1s+1s, 1s+2s+2s, 2s+1s+2s, 2s+2s+1s = 8

so and why?