
    Design a function for a patient monitoring system that calculates the total number of vital sign combinations requiring surveillance at a given severity level n, where each increasing level incorporates all previous parameter combinations plus new ones in a tetrahedral pattern of escalating complexity. The system needs to determine the exact count of vital sign parameter combinations that must be monitored at severity level n, ensuring comprehensive patient safety monitoring that grows three-dimensionally with each severity tier.
    

    
def tetrahedral_number(n):
    """
    Design a function for a patient monitoring system that calculates the total number of vital sign combinations requiring surveillance at a given severity level n, where each increasing level incorporates all previous parameter combinations plus new ones in a tetrahedral pattern of escalating complexity. The system needs to determine the exact count of vital sign parameter combinations that must be monitored at severity level n, ensuring comprehensive patient safety monitoring that grows three-dimensionally with each severity tier.
    

    """
def tetrahedral_number(n):
    """
    Design a function for a patient monitoring system that calculates the total number of vital sign combinations requiring surveillance at a given severity level n, where each increasing level incorporates all previous parameter combinations plus new ones in a tetrahedral pattern of escalating complexity. The system needs to determine the exact count of vital sign parameter combinations that must be monitored at severity level n, ensuring comprehensive patient safety monitoring that grows three-dimensionally with each severity tier.
    

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