You are laying out carpet on a 1 meter by n meter hallway. You have available two different…

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You are laying out carpet on a 1 meter by n meter hallway.

You have available two different swatches of carpet:

1×5 red carpet and 1×2 blue carpet.

Construct a recurrence with appropriate initial conditions for

the number of ways to carpet a hallway of length n.

Justify your solution.

Use as many initial conditions as you need, but no more.

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