School Awards

November 3, 2015

This counting problem appears from time to time:

There is a school that awards students who, during a given period, are never late more than once and who are never absent for three or more consecutive days. How many permutations of on-time, late and absent, with repetition, are possible for a given timeframe that will result in an award being given to a particular student. For instance, for a three-day timeframe there are 19 ways in which a student can win an award.

Your task is to solve the counting problem given above. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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