######################Problem 5###########################
def paranoid_number(n):
    """prec: n is a nonnegative integer
    postc: returns the nth paranoid number
    paranoid_number(0) = 1
    paranoid_number(1) = 3
    paranoid_number(n+2) = 5*paranoid_number(n-1) -  6*paranoid_number(n) 
    """
    if n == 0:
        return 1
    if n == 1:
        return 3
    return paranoid_number(n-1)*5 - paranoid_number(n-2)*6
def paranoid_number(n):
    """prec: n is a nonnegative integer
    postc: returns the nth paranoid number
    paranoid_number(0) = 1
    paranoid_number(1) = 3
    paranoid_number(n+2) = 5*paranoid_number(n-1) -  6*paranoid_number(n) 
    """
    if n == 0:
        return 1
    if n == 1:
        return 3
    old, new = 1,3
    for k in range(n):
        new, old = 5*new - 6*old, new
    return old
def main():
    print("*************** Problem 5 Tests **************")
    for k in range(10):
        print(paranoid_number(k))
    print(paranoid_number(100))
main()