from functools import lru_cache


@lru_cache()
def block_combinations(row_length: int, min_block_length: int = 3):
    if row_length == 0:
        return 1
    result = 0
    result = block_combinations(row_length - 1, min_block_length)
    for new_block in range(min_block_length, row_length):
        result += block_combinations(row_length - new_block - 1, min_block_length)
    if row_length >= min_block_length:
        result += 1
    return result


def euler_115():
    for n in range(1000):
        if block_combinations(n, 50) > 10**6:
            return n
    return -1


if __name__ == "__main__":
    solution = euler_115()
    print("e115.py: " + str(solution))
    assert(solution == 168)