The recurrence relation for the number of ways to lay out a walkway with slate tiles if the tiles are
red, green, or gray, so that no two red tiles are adjacent and tiles of the same color are considered
indistinguishable is taken as a =2a +2a-for n22 with initial conditions ao=1. a1-3.
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5+5+5+5-6+5+5+56-55+6666664%+6455456 46
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