Stairway

A person who can climb one, two or three steps in a single leap is trying to climb a stairway. The stairway consists of 25 steps. In how many different ways can he climb this stairway?

If the question was asked for a stairway consisting of 4 steps, the answer would be 7 (1-1-1-1, 1-1-2, 1-2-1, 2-1-1, 2-2, 1-3, 3-1).

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