Python Program to Generate Pascal’s Triangle

Last Updated on 16 March 2025

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:

\[ C(n, k) = \frac{n!}{k!(n-k)!} \]

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

Method	Approach	Pros	Cons
Loop	Builds rows iteratively	Easy to understand	Uses extra memory
Recursion	Uses binomial coefficient formula	Efficient for smaller values	Slower for large values