CACHE = {0: 0, 1: 1}

def fib_memo(n):
    if n not in CACHE:
        print("Computing new value.")
        CACHE[n] = fib_memo(n-1) + fib_memo(n-2)
    print("Fetching value from cache.")
    return CACHE[n]


start = 1
stop = 5

res = []

for i in range(start, stop+1):
    res.append(fib_memo(i))

print(res)


res2 = []

for i in range(start, stop+1):
    res2.append(fib_memo(i))

print(res2)