Sum of fourth power of first n even natural numbers

Write a program to find the sum of fourth power of first n even natural numbers. 
2⁴ + 4⁴ + 6⁴ + 8⁴ + 10⁴ +………+2n⁴
Examples:

Input:   3
Output:  1568
2⁴ +4⁴ +6⁴ = 1568

Input:   6
Output:  36400
2⁴ + 4⁴ + 6⁴ + 8⁴ + 10⁴ + 12⁴

Naive Approach :- In this Simple finding the fourth powers of the first n even natural numbers is iterate a loop from 1 to n time. Every i’th iteration store in variable and continue till (i!=n). This takes a O(N) Time Complexity.

C++

// CPP Program to find the sum of fourth powers of
// first n even natural numbers
#include <bits/stdc++.h>
using namespace std;

// calculate the sum of fourth power of first n even
// natural numbers
long long int evenPowerSum(int n)
{
    long long int sum = 0;
    for (int i = 1; i <= n; i++) {

        // made even number
        int j = 2 * i;
        sum = sum + (j * j * j * j);
    }
    return sum;
}

// Driven Program
int main()
{
    int n = 5;
    cout << evenPowerSum(n) << endl;
    return 0;
}

Java

// Java Program to find the sum of fourth powers of
// first n even natural numbers

import java.io.*;

class GFG {

    // calculate the sum of fourth power of first
    // n even natural numbers
    static long evenPowerSum(int n)
    {
        long sum = 0;
        for (int i = 1; i <= n; i++)
        {

            // made even number
            int j = 2 * i;
            sum = sum + (j * j * j * j);
        }

        return sum;
    }

    // Driven Program
    public static void main (String[] args) {

        int n = 5;
        System.out.println(evenPowerSum(n));
    }
}

/*This code is contributed by vt_m.*/

Python3

# Python3 Program to find
# the sum of fourth powers of
# first n even natural numbers

# calculate the sum of fourth
# power of first n even
# natural numbers
def evenPowerSum(n):
    sum = 0;
    for i in range(1, n + 1):

        # made even number
        j = 2 * i;
        sum = sum + (j * j * j * j);
    return sum;

# Driver Code
n = 5;
print(evenPowerSum(n));

# This is contributed by mits.

C#

// C# Program to find the sum of fourth powers of
// first n even natural numbers
using System;

class GFG {

    // calculate the sum of fourth power of
    // first n even natural numbers
    static long evenPowerSum(int n)
    {

        long sum = 0;
        for (int i = 1; i <= n; i++) {

            // made even number
            int j = 2 * i;
            sum = sum + (j * j * j * j);
        }

        return sum;
    }

    // Driven Program
    public static void Main()
    {
        int n = 5;

        Console.Write(evenPowerSum(n));
    }
}

// This code is contributed by vt_m.

PHP

<?php
// PHP Program to find the
// sum of fourth powers of
// first n even natural numbers

// calculate the sum of
// fourth power of first
// n even natural numbers
function evenPowerSum($n)
{
    $sum = 0;
    for ($i = 1; $i <= $n; $i++)
    {

        // made even number
        $j = 2 * $i;
        $sum = $sum + ($j * $j * $j * $j);
    }
    return $sum;
}

// Driver Code
$n = 5;
echo(evenPowerSum($n));

// This code is contributed by Ajit.
?>

Javascript

<script>

// JavaScript Program to find the sum of fourth powers of
// first n even natural numbers

// calculate the sum of fourth power of first n even
// natural numbers
function evenPowerSum( n)
{
    let sum = 0;
    for (let i = 1; i <= n; i++)
    {

        // made even number
        let j = 2 * i;
        sum = sum + (j * j * j * j);
    }
    return sum;
}

// Driven Program
    let n = 5;
     document.write(evenPowerSum(n));

// This code is contributed by Rajput-Ji

</script>

Output

15664

Time Complexity: O(n)
Auxiliary Space: O(1)

Efficient Approach :- An efficient solution is to use direct mathematical formula which is derived below, This takes only O(1) Time Complexity.

Sum of fourth power of first n even natural number = 8*(n*(n+1)*(2*n+1)(3*n²+3*n -1))/15 
How does this formula work? 
Sum of fourth power of natural numbers is = (n(n+1)(2n+1)(3n²+3n-1))/30 
we need even natural number so we multiply each term 2⁴
= 2⁴(1⁴ + 2⁴ + 3⁴ + ………… +n⁴) 
= (2⁴ + 4⁴ + 6⁴ + ………… +2n⁴) 
= 2⁴*(sum of fourth power natural number) 
= 16*(n*(n+1)*(2*n+1)(3*n²+3*n -1))/30 
= 8*(n*(n+1)*(2*n+1)(3*n²+3*n -1))/15 

C++

// CPP Program to find the sum of fourth powers of
// first n even natural numbers
#include <bits/stdc++.h>
using namespace std;

// calculate the sum of fourth power of first n
// even natural numbers
long long int evenPowerSum(int n)
{
    return (8 * n * (n + 1) * (2 * n + 1) *
          (3 * n * n + 3 * n - 1)) / 15;
}

// Driven Program
int main()
{
    int n = 4;
    cout << evenPowerSum(n) << endl;
    return 0;
}

Java

// JAVA Program to find the sum of fourth powers of
// first n even natural numbers

import java.io.*;

class GFG {

    // calculate the sum of fourth power of first n
    // even natural numbers
    static long evenPowerSum(int n)
    {
        return (8 * n * (n + 1) * (2 * n + 1) *
                   (3 * n * n + 3 * n - 1)) / 15;
    }

    // Driven Program
    public static void main (String[] args) {

        int n = 4;
        System.out.println(evenPowerSum(n));
    }
}

/* This code is contributed by vt_m. */

Python3

# Python3 Program to find
# the sum of fourth powers
# of first n even natural
# numbers

# calculate the sum of
# fourth power of first n
# even natural numbers
def evenPowerSum(n):
    return (8 * n * (n + 1) *
           (2 * n + 1) * (3 *
            n * n + 3 * n - 1)) / 15;

# Driver Code
n = 4;
print (int(evenPowerSum(n)));

# This code is contributed by mits

C#

// C# Program to find the sum of fourth powers of
// first n even natural numbers

using System;

class GFG {

    // calculate the sum of fourth power of first n
    // even natural numbers
    static long evenPowerSum(int n)
    {
        return (8 * n * (n + 1) * (2 * n + 1) *
                     (3 * n * n + 3 * n - 1)) / 15;
    }

    // Driven Program
    public static void Main()
    {
        int n = 4;

        Console.Write(evenPowerSum(n));
    }
}

/* This code is contributed by vt_m.*/

PHP

<?php
// PHP Program to find the
// sum of fourth powers of
// first n even natural numbers

// calculate the sum of
// fourth power of first n
// even natural numbers
function evenPowerSum($n)
{
    return (8 * $n * ($n + 1) *
           (2 * $n + 1) *
           (3 * $n * $n + 3 *
            $n - 1)) / 15;
}

// Driver Code
$n = 4;
echo(evenPowerSum($n));

// This code is contributed by Ajit.
?>

Javascript

<script>

// Javascript Program to find the sum of fourth powers of
// first n even natural numbers

// calculate the sum of fourth power of first n
// even natural numbers
    function evenPowerSum(n)
    {
        return (8 * n * (n + 1) * (2 * n + 1)
        * (3 * n * n + 3 * n - 1)) / 15;
    }

    // Driven Program


        var n = 4;
        document.write(evenPowerSum(n));

// This code is contributed by Rajput-Ji

</script>

Output

5664

Time Complexity: O(1)
Auxiliary Space: O(1)