Python Program to Generate Pascal’s Triangle

Pascal’s Triangle is a triangular arrangement of numbers where:

• The first and last number in each row is always 1.
• Each number inside the triangle is the sum of the two numbers above it.

Example of Pascal’s Triangle (First 5 Rows):

      1
     1 1
    1 2 1
   1 3 3 1
  1 4 6 4 1

In this tutorial, we will learn how to generate Pascal’s Triangle using Python.

Python Program to Generate Pascal’s Triangle

Method 1: Using Loops

def pascal_triangle(n):
    for i in range(n):
        row = [1]  # First element is always 1
        if i > 0:
            for j in range(1, i):
                row.append(prev_row[j - 1] + prev_row[j])  # Sum of two above numbers
            row.append(1)  # Last element is always 1
        print(" ".join(str(x) for x in row).center(n * 3))  # Format output
        prev_row = row  # Store current row for next iteration

# Taking user input
N = int(input("Enter the number of rows: "))

# Generating Pascal's Triangle
pascal_triangle(N)

How the Program Works

• First, we define a function pascal_triangle(n) where n is the number of rows.
• Next, we use a for loop to iterate through each row from 0 to n-1.
• Every row starts with 1 because the first and last number in Pascal’s Triangle is always 1.
• We create a list called row and set the first element as 1.
• If the row has more than one element, we calculate the middle values using:
  • current value = previous row’s left value+previous row’s right value
• We use a for loop inside to generate these values.
• Each row ends with 1, so we append 1 at the end of the row list.
• We use " ".join(str(x) for x in row).center(n * 3) to print the row in a triangular format.
• At last, we store the current row in prev_row so that we can use it to calculate the next row.

Output

Enter the number of rows: 5
       1       
      1 1      
     1 2 1     
    1 3 3 1    
   1 4 6 4 1

Method 2: Using Recursion (Mathematical Approach)

We can use binomial coefficients to calculate each element:

Where n is the row number, and k is the column index.

from math import factorial

def pascal_value(n, k):
    return factorial(n) // (factorial(k) * factorial(n - k))

def pascal_triangle(n):
    for i in range(n):
        row = [pascal_value(i, k) for k in range(i + 1)]
        print(" ".join(str(x) for x in row).center(n * 3))  # Format output

# Taking user input
N = int(input("Enter the number of rows: "))

# Generating Pascal's Triangle
pascal_triangle(N)

Comparison of Both Methods