a_0 = 1+1j
a_1 = -24

cache = {}

def a(n):
    if n == 0:
        return a_0
    elif n == 1:
        return a_1
    elif n in cache:
        return cache[n]
    else:
        result = 0.5*(a(n-1) + a(n-2))
        cache[n] = result
        return result

print(a(500))
print((1/3)*(a_0 + 2*a_1))