
    In a delivery zone where routes intersect and form triangular patterns of connections, calculate the total number of possible route combinations when n new delivery paths are added to the network, with each path creating connections with all existing routes. The number of combinations follows a tetrahedral pattern where each layer represents the additional connections formed by a new route.
    

    
def tetrahedral_number(n):
    """
    In a delivery zone where routes intersect and form triangular patterns of connections, calculate the total number of possible route combinations when n new delivery paths are added to the network, with each path creating connections with all existing routes. The number of combinations follows a tetrahedral pattern where each layer represents the additional connections formed by a new route.
    

    """
def tetrahedral_number(n):
    """
    In a delivery zone where routes intersect and form triangular patterns of connections, calculate the total number of possible route combinations when n new delivery paths are added to the network, with each path creating connections with all existing routes. The number of combinations follows a tetrahedral pattern where each layer represents the additional connections formed by a new route.
    

    """
    return n * (n + 1) * (n + 2) / 6