Problem 1. There are lines in front of grocery stores in Corvallis during the pandemic time. There are n spaces in a long row, and each space is either empty or taken by a customer. To be extra careful, a new decision has been made that people cannot stand in adjacent spaces, so there must be at least one empty space between every two customers. Let S(n) be all possible states of such a line with n spaces. For example, S(3) = 5; the possibilities are {EEE,CEE, ECE, EEC,CEC), where E denotes Empty and C denotes Customer. Write a recurrence for S(n) with its base cases, and show that your recurrence is correct. You can assume that S(0) = 1. You do not need to solve the recursion. Problem 1. There are lines in front of grocery stores in Corvallis during the pandemic time. There are n spaces in a long row, and each space is either empty or taken by a customer. To be extra careful, a new decision has been made that people cannot stand in adjacent spaces, so there must be at least one empty space between every two customers. Let S(n) be all possible states of such a line with n spaces. For example, S(3) = 5; the possibilities are {EEE,CEE, ECE, EEC,CEC), where E denotes Empty and C denotes Customer. Write a recurrence for S(n) with its base cases, and show that your recurrence is correct. You can assume that S(0) = 1. You do not need to solve the recursion