Below mentioned is the python 3 program to print the double sided stair case pattern.

Here's a Python program that prints a double-sided staircase pattern using nested loops and conditional statements: 

# Define a function to print the double-sided staircase pattern
def print_staircase(n):
    # Loop through the rows
    for i in range(n):
        # Print spaces for the left staircase
        for j in range(n - i - 1):
            print(" ", end="")
        # Print asterisks for the left staircase
        for j in range(i + 1):
            print("*", end="")
        # Print spaces between the staircases
        for j in range(n):
            if j < i:
                print(" ", end="")
            else:
                break
        # Print asterisks for the right staircase
        for j in range(n - i):
            print("*", end="")
        # Print a newline character to move to the next row
        print()

# Test the function with an input of 5
print_staircase(5)

This program defines a function called print_staircase that takes an integer n as its argument. The function then uses nested loops to print the double-sided staircase pattern. The outer loop iterates through the rows, while the inner loops print the spaces and asterisks for each staircase. The conditional statement inside the loop prints spaces between the staircases. Finally, a newline character is printed to move to the next row.

When the function is called with an input of 5, it prints the following output: 

   *    *****
   **    ****
  ***    ***
 ****    **
*****    *

This pattern consists of two staircases, one on the left and one on the right, with spaces between them. The length of each staircase is equal to the row number, and the total height of the pattern is equal to n.