## (Solved) Problem 1: Let Wn be the number of strings of length n formed

Problem 1: Let Wn be the number of strings of length n formed from letters A, B, C, and D that do notncontain a substring AA, BA or CA. For example, for n = 2, all the strings with this property areAB, AC, AD, BB, BC, BD, CB, CC, CD, DA, DB, DC, DDand thus W2 = 13. (Note that W0 = 1, because the empty string satisfies the condition.)

(a) Derive a recurrence relation for the numbers Wn. Justify it.

(b) Find the formula for the numbers Wn by solving this recurrence. Show your work.

a) Consider how to get strings with n+1 characters from strings with n characters.

For any of Wn strings with n characters, we can add B,C, D to it to get strings with n+1 characters thus

have

3Wn...

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This question was answered on: Oct 15, 2019

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