from functools import lru_cache


@lru_cache
def combs(xs, first=False):
    if xs == (0, 0, 0, 0):
        return 1
    
    c = 0
    z, o, a, r = xs

    if (not first) and z > 0:
        c += combs((z - 1, o, a, r))
    if o > 0:
        c += combs((z, o - 1, a, r))
    if a > 0:
        c += combs((z, o, a - 1, r))
    if r > 0:
        c += 13 * combs((z, o, a, r - 1))
    return c


def euler_162():
    t = 0
    for n in range(17):
        for z in range(1, n + 1):
            for o in range(1, n + 1):
                for a in range(1, n + 1):
                    r = n - z - o - a
                    if not r >= 0:
                        continue
                    t += combs((z, o, a, r), True)
    return hex(t)[2:].upper()


if __name__ == "__main__":
    solution = euler_162()
    print("e162.py: " + str(solution))
    assert(solution == "3D58725572C62302")