
    Design a function for a social network's friend recommendation system that calculates the total potential connection patterns by analyzing alternating layers in a user's social graph up to a specified depth level n, considering only the even-numbered degrees of separation. The function should compute this by summing the binomial coefficients at even indices up to level n, where each coefficient represents the possible connection patterns at that degree of separation.
    

    
import math

def even_binomial_Coeff_Sum(n):
    """
    Design a function for a social network's friend recommendation system that calculates the total potential connection patterns by analyzing alternating layers in a user's social graph up to a specified depth level n, considering only the even-numbered degrees of separation. The function should compute this by summing the binomial coefficients at even indices up to level n, where each coefficient represents the possible connection patterns at that degree of separation.
    

    """
import math

def even_binomial_Coeff_Sum(n):
    """
    Design a function for a social network's friend recommendation system that calculates the total potential connection patterns by analyzing alternating layers in a user's social graph up to a specified depth level n, considering only the even-numbered degrees of separation. The function should compute this by summing the binomial coefficients at even indices up to level n, where each coefficient represents the possible connection patterns at that degree of separation.
    

    """
    return 1 << n - 1