Write a recurrence relation and initial conditions for the number S n of sequences of Nickles, dimes and quarters that can be inserted into a vending machine to purchase a soft drink costing 5n cents....

Write a recurrence relation and initial conditions for the number S_n
of sequences of Nickles, dimes and quarters that can be inserted into a vending machine to purchase a soft drink costing 5n cents. How many sequences are there for a drink costing 50 cents?