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Let hn be the number of ways to cover a 1 × n board using only...

Let hn be the number of ways to cover a 1 × n board using only 1 × 1 tiles, red or blue 3 × 1 tiles, red, blue, or green 4 × 1 tiles, and 5 × 1 tiles. Find a recurrence relation for hn along with enough enough initial conditions to allow one to compute the entire sequence.

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