A professor who is late for class is running up a staircase of n stairs. The professor takes steps that cover either 2,

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A professor who is late for class is running up a staircase of n stairs. The professor takes steps that cover either 2,

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A Professor Who Is Late For Class Is Running Up A Staircase Of N Stairs The Professor Takes Steps That Cover Either 2 1
A Professor Who Is Late For Class Is Running Up A Staircase Of N Stairs The Professor Takes Steps That Cover Either 2 1 (73.1 KiB) Viewed 40 times
A professor who is late for class is running up a staircase of n stairs. The professor takes steps that cover either 2, 4 or 5 stairs. But steps of 4 or 5 stairs are exhausting. So after each step of 5, the professor takes a step that covers only 2 stairs. After a step of 4 stairs, the professor makes a step of 2 or 4 stairs, but after two consecutive steps of 4 stairs he can only make a step of 2 stairs. Find a recurrence relation for an, the number of different ways for the professor to ascend the n-staircase. Justify your result. [6]
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