Question

In the Island of Combinatorica, a valid drivers license of length n can be constructed in 3 ways: (a) Starting with A followed by any valid drivers license of length n -1 (b) Starting with one of the two-character strings 1A, 1B, 1C,1D, 1E, or 1F followed by any drivers license of length n-2 (c) Starting with 0 and followed by any ternary string (alphabet 0, 1,2]) of lengthn-1. Find a recurrence for the number g(n) of valid drivers licenses of length n and then solve this recurrence relation to get a closed form solution. You can assume that g(0) 1.

Answer 1

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