from rt import *
######################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 5*paranoid_number(n-1) - 6*paranoid_number(n - 2)
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 = 1
    new = 3
    for k in range(n):
        new, old = 5*new - 6*old, new
    return old 
def main():
    print("*************** Problem 5 Tests **************")
    print(run_test(paranoid_number, 1, [0]))
    print(run_test(paranoid_number, 3, [1]))
    print(run_test(paranoid_number, 729, [6]))
    for k in range(1,11):
        print(paranoid_number(k))
    print(paranoid_number(10000))
main()