Is this recursive function an acceptable use-case for mutable default arguments?

I have a function that recursively finds a solution to a maze represented by a 2D array. I declared all the default arguments in a way that would allow me to call this function from main without passing any arguments. One of these default arguments is an empty list, which I understand is bad practice. I'm wondering if this is a valid use-case of a mutable default argument, or if there's a better way to do this:

def solve_maze(self, i=0, j=0, path=[]):
    if (i, j) in self.memory:
        return False
    if self.maze[i][j] == 'D':
        return path[:-1]
    if not (directions := self.get_directions(i, j, [[i, j]] + path)):
        self.memory.append((i, j))
        return False
    move = {'l': [i, j-1], 'u': [i-1, j], 'r': [i, j+1], 'd': [i+1, j]}
    for k in range(len(directions)):
        best_dir = directions[k]
        if solution := self.solve_maze(move[best_dir][0], move[best_dir][1], [[i, j]] + path):
            return solution
    self.memory.append((i, j))
    return False

This function behaves exactly how I need it, so I don't need help making it work. Using this mutable default is not causing me issues. This is simply a personal curiosity on "proper Python coding".

I do realize the obvious solution is something akin to this:

def solve_maze(self, i=0, j=0, path=None):
    if not path:
        path = []

But this just adds clutter to my code. I'm curious what the "correct" way to do this is.