
    Given a user's social network depth level n, calculate the total number of potential friend recommendations that occur at even-numbered connection degrees within that network depth, where each degree's recommendation count follows the pattern of binomial coefficients. The recommendation count at each degree represents the number of unique ways mutual connections can form at that level, and we only sum the counts from even-numbered degrees up to the given depth n.
    

    
import math

def even_binomial_Coeff_Sum(n):
    """
    Given a user's social network depth level n, calculate the total number of potential friend recommendations that occur at even-numbered connection degrees within that network depth, where each degree's recommendation count follows the pattern of binomial coefficients. The recommendation count at each degree represents the number of unique ways mutual connections can form at that level, and we only sum the counts from even-numbered degrees up to the given depth n.
    

    """
import math

def even_binomial_Coeff_Sum(n):
    """
    Given a user's social network depth level n, calculate the total number of potential friend recommendations that occur at even-numbered connection degrees within that network depth, where each degree's recommendation count follows the pattern of binomial coefficients. The recommendation count at each degree represents the number of unique ways mutual connections can form at that level, and we only sum the counts from even-numbered degrees up to the given depth n.
    

    """
    return 1 << n - 1