
    Design a function that calculates the total number of possible patient admission-discharge patterns in a hospital's capacity planning model by summing the even-indexed combinations across n time periods. The function should take the number of time periods n as input and compute the sum of binomial coefficients at even indices, which represent the statistically significant admission patterns used in bed occupancy forecasting. This calculation is essential for optimizing hospital bed allocation and improving admission scheduling efficiency.
    

    
import math

def even_binomial_Coeff_Sum(n):
    """
    Design a function that calculates the total number of possible patient admission-discharge patterns in a hospital's capacity planning model by summing the even-indexed combinations across n time periods. The function should take the number of time periods n as input and compute the sum of binomial coefficients at even indices, which represent the statistically significant admission patterns used in bed occupancy forecasting. This calculation is essential for optimizing hospital bed allocation and improving admission scheduling efficiency.
    

    """
import math

def even_binomial_Coeff_Sum(n):
    """
    Design a function that calculates the total number of possible patient admission-discharge patterns in a hospital's capacity planning model by summing the even-indexed combinations across n time periods. The function should take the number of time periods n as input and compute the sum of binomial coefficients at even indices, which represent the statistically significant admission patterns used in bed occupancy forecasting. This calculation is essential for optimizing hospital bed allocation and improving admission scheduling efficiency.
    

    """
    return 1 << n - 1