from functools import lru_cache


@lru_cache()
def block_combinations(row_length: int):

    if row_length == 0:
        return 1

    min_block_length = 3
    result = 0

    # Moving from left to right. Let's say we have four spaces (____), then
    # there are three options

    # Use a blank:
    #   -___
    result = block_combinations(row_length - 1)
         
    # Or add 3:
    #   ooo_ 
    # For this case, the issue is that if we call block_combinations again with
    # _, then it could happen that we will up with further o and double count.
    # Therefore, for all cases where the spaces are not all filled, we will add
    # a space.
    for new_block in range(min_block_length, row_length):
        result += block_combinations(row_length - new_block - 1)

    # Or add 4:
    #   oooo
    if row_length >= min_block_length:
        result += 1
         
    return result


def euler_114():
    assert block_combinations(0) == 1
    assert block_combinations(1) == 1
    assert block_combinations(2) == 1
    assert block_combinations(3) == 2
    assert block_combinations(4) == 4
    assert block_combinations(7) == 17
    return block_combinations(50)


if __name__ == "__main__":
    solution = euler_114()
    print("e114.py: " + str(solution))
    # assert(solution == 0)