Ways of Stepping One, Two, or Three Stairs Up a Stairway

For a person who can climb stairs either one, two, or three stairs at a time there are many ways of climbing a stairway with stairs. For a stairway consisting of four stairs, there are the following seven ways:

{{1,1,1,1}, {1,1,2}, {1,2,1}, {2,1,1}, {2,2}, {1,3}, {3,1}}.

This Demonstration shows the combinations and counts the permutations of these combinations for stairways of different lengths. It also shows a simpler way of finding the number of different ways of climbing the stairways using the Tribonacci series.