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Math 55: Discrete Mathematics

Math 55: Discrete MathematicsUC Berkeley, Spring 2012 Homework # 9, due Wednesday, April many ways are there to pay a bill of17pesos using a currencywith coins of values of1peso,2pesos,5pesos, and10pesos, and withbills with values of5pesos and10pesos?Letandenote the number of ways to pay a bill ofnpesos. Thenan= 0 forn <0, anda0= 1, and we have the recurrence relationan=an 1+an 2+ 2 an 5+ 2 an 10forn recurrence relation gives the following sequence:n1 2 3 45678an1 2 3 5 10 17 31 548 9 10 11 12 131415161754 95 171 302 539 955 1694 3011 5343 9494 Hence there are 9494 ways to pay a bill of 17 ) Find a recurrence relation for the number of bit strings of lengthnthat contain three ) What are initial conditions?

54 95 171 302 539 955 1694 3011 5343 9494 Hence there are 9494 ways to pay a bill of 17 pesos. 8.1.8 a) Find a recurrence relation for the number of bit strings of length nthat contain three consecutive 0s. b) What are initial conditions? c) How many bit strings of length seven contain three consecutive 0s? Let a

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