Sum of all the numbers present at given level in Pascal’s triangle

Given a level L. The task is to find the sum of all the integers present at the given level in Pascal’s triangle .

A Pascal triangle with 6 levels is shown below: 

1 
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1 

Examples:

Input: L = 3 
Output: 4 
1 + 2 + 1 = 4

Input: L = 2 
Output:2 

Approach: If we observe carefully the series of the sum of levels will go on like 1, 2, 4, 8, 16…., which is a GP series with a = 1 and r = 2.
Therefore, sum of Lth level is L’th term in the above series. 

Lth term = 2L-1

Below is the implementation of the above approach: 

C++

// C++ implementation of the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to find sum of numbers at
// Lth level in Pascals Triangle
int sum(int h)
{
    return pow(2, h - 1);
}

// Driver Code
int main()
{
    int L = 3;

    cout << sum(L);

    return 0;
}

Java

// Java implementation of the approach
class GFG
{

    // Function to find sum of numbers at
    // Lth level in Pascals Triangle
    static int sum(int h)
    {
        return (int)Math.pow(2, h - 1);
    }

    // Driver Code
    public static void main (String[] args)
    {
        int L = 3;

        System.out.println(sum(L));
    }
}

// This code is contributed by AnkitRai01

Python3

# Python3 implementation of the above approach

# Function to find sum of numbers at
# Lth level in Pascals Triangle
def summ(h):
    return pow(2, h - 1)

# Driver Code
L = 3

print(summ(L))

# This code is contributed by mohit kumar

C#

// C# implementation of the approach
using System;

class GFG
{

    // Function to find sum of numbers at
    // Lth level in Pascals Triangle
    static int sum(int h)
    {
        return (int)Math.Pow(2, h - 1);
    }

    // Driver Code
    public static void Main ()
    {
        int L = 3;

        Console.WriteLine(sum(L));
    }
}

// This code is contributed by anuj_67..

Javascript

<script>

// Javascript implementation of the above approach

// Function to find sum of numbers at
// Lth level in Pascals Triangle
function sum(h)
{
    return Math.pow(2, h - 1);
}

// Driver Code
var L = 3;

document.write(sum(L));

</script>

Output:

4

Time Complexity: O(log₂L) because it is using pow function
Auxiliary Space: O(1)