
    In a multi-tier patient monitoring system, determine the total number of vital sign combinations that need to be monitored at a given risk level tier n, where each tier adds an additional vital sign that must be cross-monitored with all previous combinations. The monitoring load increases following a tetrahedral pattern, where tier n requires monitoring all possible combinations of vital signs from levels 1 through n.
    

    
def tetrahedral_number(n):
    """
    In a multi-tier patient monitoring system, determine the total number of vital sign combinations that need to be monitored at a given risk level tier n, where each tier adds an additional vital sign that must be cross-monitored with all previous combinations. The monitoring load increases following a tetrahedral pattern, where tier n requires monitoring all possible combinations of vital signs from levels 1 through n.
    

    """
def tetrahedral_number(n):
    """
    In a multi-tier patient monitoring system, determine the total number of vital sign combinations that need to be monitored at a given risk level tier n, where each tier adds an additional vital sign that must be cross-monitored with all previous combinations. The monitoring load increases following a tetrahedral pattern, where tier n requires monitoring all possible combinations of vital signs from levels 1 through n.
    

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