Question

Discrete math

4. Popeye and Olive Oyl frequently send each other text messages that are just contiguous strings of the three emojis , , and . For instance, one particular length-5 emoji string might be e (a) Find a recurrence relation for the number of possible length-n emoji strings that do not contain two consecutive winkey emojis, (b) What are the initial conditions for the recurrence relation? (c) Find a closed-form solution to the recurrence relation you found in part (a) by solving for the roots of the characteristic polynomial and then using initial conditions to determine the constants. (d) Use your closed form expression to determine the number of length-7 emoji strings that do not contain 2 consecutive winkey emojis. Note: You may use Python to help you answer this question.]

Answer 1

Solution:

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0, te closed tormula is, an 2 2+13 243 Fordゞ Noef strings ef lengは子ttat do not ntain