
    Design a function for a smart medication organizer that calculates the total number of medication slots needed in a hexagonal layout, where each expanding ring represents a time period and contains an increasing number of compartments around the center slot. Given the sequential position of a dose schedule (n), determine the cumulative number of medication slots required to accommodate all doses up to and including the nth time period.
    

    
def centered_hexagonal_number(n):
    """
    Design a function for a smart medication organizer that calculates the total number of medication slots needed in a hexagonal layout, where each expanding ring represents a time period and contains an increasing number of compartments around the center slot. Given the sequential position of a dose schedule (n), determine the cumulative number of medication slots required to accommodate all doses up to and including the nth time period.
    

    """
def centered_hexagonal_number(n):
    """
    Design a function for a smart medication organizer that calculates the total number of medication slots needed in a hexagonal layout, where each expanding ring represents a time period and contains an increasing number of compartments around the center slot. Given the sequential position of a dose schedule (n), determine the cumulative number of medication slots required to accommodate all doses up to and including the nth time period.
    

    """
    return 3 * n * (n - 1) + 1