
    In a hospital emergency room with hexagonal-shaped waiting zones, determine the total number of patient seats needed when expanding outward from a central seat, where each new ring of seats follows a centered hexagonal pattern to maintain efficient patient flow. The solution will help hospital administrators calculate capacity for the nth expansion ring, ensuring adequate seating during peak hours.
    

    
def centered_hexagonal_number(n):
    """
    In a hospital emergency room with hexagonal-shaped waiting zones, determine the total number of patient seats needed when expanding outward from a central seat, where each new ring of seats follows a centered hexagonal pattern to maintain efficient patient flow. The solution will help hospital administrators calculate capacity for the nth expansion ring, ensuring adequate seating during peak hours.
    

    """
def centered_hexagonal_number(n):
    """
    In a hospital emergency room with hexagonal-shaped waiting zones, determine the total number of patient seats needed when expanding outward from a central seat, where each new ring of seats follows a centered hexagonal pattern to maintain efficient patient flow. The solution will help hospital administrators calculate capacity for the nth expansion ring, ensuring adequate seating during peak hours.
    

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