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Suppose a vending machine accepts $1 bills and $1 gold coins, as well as $3 bills, $3 silver coin...

Suppose a vending machine accepts $1 bills and $1 gold coins, as well as $3 bills, $3 silver coins and $3 gold coins. a. Write a recurrence for the number of ways to deposit n dollars into the machine, where the order in which the coins and bills are deposited matters. b. What are the initial conditions? c. How many ways are there to deposit $5 into the machine?

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