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Question: a frog is to climb a staircase with n steps...

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A frog is to climb a staircase with n steps. The frog can jump up 1,2, or 3 steps at once. However, the frog gets tired after a 3-step jump, and therefore cannot make consecutive 3-step jumps. Determine a recurrence relation for an, the number of ways in which the frog can jump up the staircase with n steps.

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