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  3. 2 express the solution to the following counting problem in...

Question: 2 express the solution to the following counting problem in...

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2. Express the solution to the following counting problem in terms of a difference equation, then use a generating function to solve the difference equation to give an explicit solution: A decorator is placing a row of coloured tiles side by side along the top of a bathroom wall. They have a choice of 1cm long tiles in either black or white, or else 2 cm long tiles in red, blue or green. How many different patterns of tiles are possible if the wall is n cm long?
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