Maths Olympiad Prep

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, 2021

Combinatorics Difficulty 5.0 AIME, harder Prove it United Kingdom

During an early morning drive to work, Simon encountered nn sets of traffic lights, each set being red, amber or green as he approached it. He noticed that consecutive lights were never the same colour. Given that he saw at least two red lights, find a simplified expression, in terms of nn, for the number of possible sequences of colours Simon could have seen.

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