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

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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:
Contributed by: Noel Patson (September 2009)
Open content licensed under CC BY-NC-SA
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"Ways of Stepping One, Two, or Three Stairs Up a Stairway"
http://demonstrations.wolfram.com/WaysOfSteppingOneTwoOrThreeStairsUpAStairway/
Wolfram Demonstrations Project
Published: September 22 2009