
    In a medical clinic's scheduling system, you need to develop a function that optimizes appointment slot distribution based on historical no-show patterns. Given a total number of available slots in a scheduling block, the system needs to calculate the sum of progressively paired time slots, where each subsequent pair reduces the available slots by 2, continuing until no slots remain available for pairing. For example, if there are 6 slots, the calculation would sum 6 + 4 + 2, representing the weighted distribution of appointment pairs. This calculation helps determine the optimal arrangement of appointments to minimize schedule gaps caused by potential no-shows. The function should work with any positive number of initial appointment slots, handling both even and odd total slot counts.
    

    
def sum_series(n):
    """
    In a medical clinic's scheduling system, you need to develop a function that optimizes appointment slot distribution based on historical no-show patterns. Given a total number of available slots in a scheduling block, the system needs to calculate the sum of progressively paired time slots, where each subsequent pair reduces the available slots by 2, continuing until no slots remain available for pairing. For example, if there are 6 slots, the calculation would sum 6 + 4 + 2, representing the weighted distribution of appointment pairs. This calculation helps determine the optimal arrangement of appointments to minimize schedule gaps caused by potential no-shows. The function should work with any positive number of initial appointment slots, handling both even and odd total slot counts.
    

    """
def sum_series(n):
    """
    In a medical clinic's scheduling system, you need to develop a function that optimizes appointment slot distribution based on historical no-show patterns. Given a total number of available slots in a scheduling block, the system needs to calculate the sum of progressively paired time slots, where each subsequent pair reduces the available slots by 2, continuing until no slots remain available for pairing. For example, if there are 6 slots, the calculation would sum 6 + 4 + 2, representing the weighted distribution of appointment pairs. This calculation helps determine the optimal arrangement of appointments to minimize schedule gaps caused by potential no-shows. The function should work with any positive number of initial appointment slots, handling both even and odd total slot counts.
    

    """
    if n < 1:
        return 0
    else:
        return n + sum_series(n - 2)