def tiles(size):
    """ Returns the number of tiles for a square of the given size. """
    return size * 4 - 4


def tiles_for_outer(size):
    """ Returns the number of tiles for all possible laminae given the size of
    the outermost ring. """

    n_outer = tiles(size)
    r = [n_outer]
    for ni in range(size - 2, 2, -2):
        n_outer += tiles(ni)
        r.append(n_outer)
    return r


def count_tiles(size, n_max):

    """ Count how many possible laminae with a size smaller the `n_max` are
    possible for the given outermost ring `size`. """

    n_outer = tiles(size)
    if n_outer > n_max:
        return 0

    count = 1
    for ni in range(size - 2, 2, -2):
        n_outer += tiles(ni)
        if n_outer > n_max:
            break
        count += 1
    return count


def euler_173():
    assert tiles(3) == 8
    assert tiles(4) == 12
    assert tiles(6) == 20
    assert tiles(9) == 32

    count = 0
    n_max = 10**6
    edge_length = 3
    for edge_length in range(3, n_max):
        if tiles(edge_length) > n_max:
            break
        count += count_tiles(edge_length, n_max)
    return count


if __name__ == "__main__":
    solution = euler_173()
    print("e173.py: " + str(solution))
    assert solution == 1572729