from functools import lru_cache


@lru_cache()
def block_combinations(row_length: int, block_length: int = 3):
    if row_length < 0:
        return 0

    if row_length == 0:
        return 1

    result = block_combinations(row_length - 1, block_length)
    result += block_combinations(row_length - block_length, block_length)
    return result


def solve(row_length: int):
    r = block_combinations(row_length, 2) - 1
    r += block_combinations(row_length, 3) - 1
    r += block_combinations(row_length, 4) - 1
    return r


def euler_116():
    return solve(50)


if __name__ == "__main__":
    solution = euler_116()
    print("e116.py: " + str(solution))
    assert(solution == 20492570929)