# Python Program to print the pascal’s triangle for n number of rows

In this simple python program, we need to solve a  pascals triangle. It's a pattern-based python program.

To understand this example, you should have knowledge of the following Python programming topics:

## What is the pascals triangle?

In this python program, we need to print one of the most interesting number patterns called pascal's triangle. Pascal triangle is in a triangle shape pattern of numbers with the topmost is a 1. Then each number is the sum of two numbers above the resultant number.

Pascal's triangle is defined as a triangular array of binomial coefficients. Pascal's triangle is symmetrical, which means the triangle's left side will be the same as the triangle's right side.

## How to solve pascal's triangle in python?

To implement this pascal's triangle logic into the python program, we accept the number of rows from the user. Then we initialize a list, and we append 1 to all the sublists in the triangle. Now we are opening a `for loop` in python from 1 to row number. Then we calculate the sub-list elements by using the sum of previous elements of the triangle, ie. a[i-1][j-1]+a[i-1][j]

Let us take an example of the second row of the pascal triangle, then the 'i' will be 2, and j will be 1 for the first element in row 2. So using the formula [2-1][1-1]+[2-1][1], which is equal to 1. Then finally, we use another `for loop` for printing the pascal's triangle in the correct pattern.

We are using a format method in python language here to print in the proper way of pascal's triangle. The `format ()` method is a built-in method in python, which returns a formatted output specified in the format parameter. The syntax for `format()` the method is "`format(value,[format_spec])`" format method takes two parameters in which one is the value to be formatted, and the other is the specifier, which mentions how the value to be formatted in python.

### ALGORITHM

STEP 1: Accept the number of rows from the user.

STEP 2: Initialize a list using the python method.

STEP 3: Open a `for loop` till the number n and append all elements to 1 to all sublists.

STEP 4: Open the nested `for loop` to calculate each element in the sublist using the formula (a[i-1][j-1]+a[i-1][j]) [ we described how the formula works in description]

STEP 5: Use another `for loop` to print the elements, and we use the format method to print it pascal's triangle format using python basic syntax.

## Python Source Code

```                                          ```n=int(input("Enter number of rows: "))
a=[]
for i in range(n):
a.append([])
a[i].append(1)
for j in range(1,i):
a[i].append(a[i-1][j-1]+a[i-1][j])
if(n!=0):
a[i].append(1)
print("Pascal's triangle of",n,"rows is")
for i in range(n):
print("   "*(n-i),end=" ",sep=" ")
for j in range(0,i+1):
print('{0:6}'.format(a[i][j]),end=" ",sep=" ")
print()```
```

## OUTPUT

```Enter number of rows: 3
Pascal's triangle of 3 rows is
1
1      1
1     2     1 ```
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