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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.


	Contributed by: Noel Patson
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Puzzle taken from Stairway.

Tribonacci Number (Wolfram MathWorld)

"Ways of Stepping One, Two, or Three Stairs Up a Stairway" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/WaysOfSteppingOneTwoOrThreeStairsUpAStairway/

Contributed by: Noel Patson

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