
    Given a number of overlapping peak periods in an emergency room's schedule, calculate the total number of staff members needed when each subsequent time period requires one additional healthcare worker than the previous period to maintain optimal patient care. The staffing pattern follows a tetrahedral progression where the first period needs one staff member, the second needs additional staff for two periods, the third needs additional staff for three periods, and so on.
    

    
def tetrahedral_number(n):
    """
    Given a number of overlapping peak periods in an emergency room's schedule, calculate the total number of staff members needed when each subsequent time period requires one additional healthcare worker than the previous period to maintain optimal patient care. The staffing pattern follows a tetrahedral progression where the first period needs one staff member, the second needs additional staff for two periods, the third needs additional staff for three periods, and so on.
    

    """
def tetrahedral_number(n):
    """
    Given a number of overlapping peak periods in an emergency room's schedule, calculate the total number of staff members needed when each subsequent time period requires one additional healthcare worker than the previous period to maintain optimal patient care. The staffing pattern follows a tetrahedral progression where the first period needs one staff member, the second needs additional staff for two periods, the third needs additional staff for three periods, and so on.
    

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