Code Guru | Python Solution

ZERO_POS = ZERO_X, ZERO_Y = (1, 3)
MIN, MAX = 0, 9
MIN_X, MIN_Y = 0, 0
MAX_X, MAX_Y = 2, 2
EMPTY_DIR = None, None

# For testing...
def main():
    print(amount_call(int(input("Enter input: "))))

# Answer to question:
def amount_call(length):
    res = 0
    for i in range(10):
        res += amount_to_call_helper(length, *get_location(i))
    return res

# Helper functions
def amount_to_call_helper(length, x, y):
    # Base for recursion:
    if length == 1:
        return 1
    # Loop possible directions
    res = 0
    for dir_func in direction_functions:
        if not dir_func(x, y) == EMPTY_DIR:
            res += amount_to_call_helper(length - 1, *dir_func(x, y))
    return res

# Parser function
def get_location(cell):
    # Zero is special:
    if cell == 0:
        return ZERO_POS
    if MIN <= cell <= MAX:
        cell_x = (cell - 1) % 3
        cell_y = int((cell - 1) / 3)
        return cell_x, cell_y
    return (-1, -1)

# Location function
def can_go_down_right(x, y):
    if is_valid(x + 1, y + 2):
        return x + 1, y + 2
    return None, None

def can_go_down_left(x, y):
    if is_valid(x - 1, y + 2):
        return x - 1, y + 2
    return None, None

def can_go_up_right(x, y):
    if is_valid(x + 1, y - 2):
        return x + 1, y - 2
    return None, None

def can_go_up_left(x, y):
    if is_valid(x - 1, y - 2):
        return x - 1, y - 2
    return None, None

def can_go_right_up(x, y):
    if is_valid(x + 2, y - 1):
        return x + 2, y - 1
    return None, None

def can_go_right_down(x, y):
    if is_valid(x + 2, y + 1):
        return x + 2, y + 1
    return None, None

def can_go_left_up(x, y):
    if is_valid(x - 2, y - 1):
        return x - 2, y - 1
    return None, None

def can_go_left_down(x, y):
    if is_valid(x - 2, y + 1):
        return x - 2, y + 1
    return None, None

def is_valid(x, y):
    return MIN_X <= x <= MAX_X and MIN_Y <= y <= MAX_Y or (x, y) == ZERO_POS

# Assign all functions into a simple list
direction_functions = [
    can_go_down_left,
    can_go_down_right,
    can_go_left_down,
    can_go_left_up,
    can_go_right_down,
    can_go_right_up,
    can_go_up_left,
    can_go_up_right
]

if __name__ == "__main__":
    main()