
    Given n bus route segments in a city's transportation network, calculate the total number of optimal scheduling combinations by summing up the even-indexed route distribution patterns (represented by binomial coefficients). This calculation helps determine the most balanced way to distribute buses across different time slots while maintaining service efficiency.
    

    
import math

def even_binomial_Coeff_Sum(n):
    """
    Given n bus route segments in a city's transportation network, calculate the total number of optimal scheduling combinations by summing up the even-indexed route distribution patterns (represented by binomial coefficients). This calculation helps determine the most balanced way to distribute buses across different time slots while maintaining service efficiency.
    

    """
import math

def even_binomial_Coeff_Sum(n):
    """
    Given n bus route segments in a city's transportation network, calculate the total number of optimal scheduling combinations by summing up the even-indexed route distribution patterns (represented by binomial coefficients). This calculation helps determine the most balanced way to distribute buses across different time slots while maintaining service efficiency.
    

    """
    return 1 << n - 1