# Sum of fourth powers of first n odd natural numbers

• Last Updated : 19 Oct, 2022

Write a program to find sum of fourth power of first n odd natural numbers.
14 + 34 + 54 + 74 + 94 + 114 ………….+(2n-1)4
Examples:

```Input  :   3
Output :   707
14 +34 +54 =  707
Input  :   6
Output :   24310
14 + 34 + 54 + 74 + 94 + 114 ```

Naive Approach: – In this Simple finding the fourth power of the first n odd natural numbers is to iterate a loop from 1 to n times, and result store in variable sum.
Ex.-n=3 then, (1*1*1*1)+(3*3*3*3)+(5*5*5*5) = 707

## C++

 `// CPP Program to find the sum of fourth powers``// of first n odd natural numbers``#include ``using` `namespace` `std;` `// calculate the sum of fourth power of first``// n odd natural numbers``long` `long` `int` `oddNumSum(``int` `n)``{``    ``int` `j = 0;``    ``long` `long` `int` `sum = 0;``    ``for` `(``int` `i = 1; i <= n; i++) {``        ``j = (2 * i - 1);``        ``sum = sum + (j * j * j * j);``    ``}``    ``return` `sum;``}` `// Driven Program``int` `main()``{``    ``int` `n = 6;``    ``cout << oddNumSum(n) << endl;``    ``return` `0;``}`

## Java

 `// Java Program to find the``// sum of fourth powers of``// first n odd natural numbers``import` `java.io.*;` `class` `GFG {` `    ``// calculate the sum of``    ``// fourth power of first``    ``// n odd natural numbers``    ``static` `long` `oddNumSum(``int` `n)``    ``{``        ``int` `j = ``0``;``        ``long` `sum = ``0``;``        ``for` `(``int` `i = ``1``; i <= n; i++) {``            ``j = (``2` `* i - ``1``);``            ``sum = sum + (j * j * j * j);``        ``}``        ``return` `sum;``    ``}` `    ``// Driven Program``    ``public` `static` `void` `main(String args[])``    ``{``        ``int` `n = ``6``;``        ``System.out.println(oddNumSum(n));``    ``}``}` `// This code is contributed``// by Nikita tiwari.`

## Python 3

 `# Python 3 Program to find the``# sum of fourth powers of``# first n odd natural numbers` `# calculate the sum of``# fourth power of first ``# n odd natural numbers``def` `oddNumSum(n) :``    ``j ``=` `0``    ``sm ``=` `0``    ``for` `i ``in` `range``(``1``, n ``+` `1``) :``        ``j ``=` `(``2` `*` `i ``-` `1``)``        ``sm ``=` `sm ``+` `(j ``*` `j ``*` `j ``*` `j)``    ` `    ``return` `sm``    ` `# Driven Program``n ``=` `6``;``print``(oddNumSum(n))`  `# This code is contributed``# by Nikita tiwari.`

## C#

 `// C# Program to find the``// sum of fourth powers of``// first n odd natural numbers``using` `System;` `class` `GFG {` `    ``// calculate the sum of``    ``// fourth power of first``    ``// n odd natural numbers``    ``static` `long` `oddNumSum(``int` `n)``    ``{``        ``int` `j = 0;``        ``long` `sum = 0;``        ``for` `(``int` `i = 1; i <= n; i++) {``            ``j = (2 * i - 1);``            ``sum = sum + (j * j * j * j);``        ``}``        ``return` `sum;``    ``}` `    ``// Driven Program``    ``public` `static` `void` `Main()``    ``{``        ``int` `n = 6;``        ``Console.Write(oddNumSum(n));``    ``}``}` `// This code is contributed by``// vt_m.`

## PHP

 ``

## Javascript

 ``

Output:

`24310`

Complexity Analysis:
Time Complexity : O(N)

Space Complexity: O(1) as no extra space is used

Efficient Approach :- An efficient solution is to use direct mathematical formula which is :

Fourth power natural number = (14 + 24 + 34 + ………… +n4
= (n(n+1)(2n+1)(3n2+3n-1))/30
Fourth power even natural number = (24 + 44 + 64 + ………… +2n4
= 8(n(n+1)(2n+1)(3n2+3n-1))/15;
We need odd natural number so we subtract the
(Fourth power odd natural number) = (Fourth power first n natural number) – (Fourth power even natural number)
= (14 + 24 + 34 + ………… +n4) – (24 + 44 + 64 + ………… +2n4
= (14 + 34 + 54 + ………… +(2n-1)4
drives formula
= (2n(2n+1)(4n+1)(12n2+6n-1))/30 – (8(n(n+1)(2n+1)(3n2+3n -1)))/15
= 2n(2n+1)/30[(4n+1)(12n2+6n-1) – ((8n+8)((3n2+3n-1))]
= n(2n+1)/15[(48n3 + 24n 2 – 4n + 12n2 + 6n -1) – (24n3 + 24n 2 – 8n + 24n2 + 24n -8) ]
= n(2n+1)/15[24n3 – 12n2 – 14n + 7]

`    Sum of fourth power of first n odd numbers =  n(2n+1)/15[24n3 - 12n2 - 14n + 7]`

## C++

 `// CPP Program to find the sum of fourth powers``// of first n odd natural numbers``#include ``using` `namespace` `std;` `// calculate the sum of fourth power of first``// n odd natural numbers``long` `long` `int` `oddNumSum(``int` `n)``{``    ``return` `(n * (2 * n + 1) *``    ``(24 * n * n * n - 12 * n``    ``* n - 14 * n + 7)) / 15;``}` `// Driven Program``int` `main()``{``    ``int` `n = 4;``    ``cout << oddNumSum(n) << endl;``    ``return` `0;``}`

## Java

 `// Java Program to find the sum of``// fourth powers of first n odd``// natural numbers``class` `GFG {``    ` `    ``// calculate the sum of fourth``    ``// power of first n odd natural``    ``// numbers``    ``static` `long` `oddNumSum(``int` `n)``    ``{``        ``return` `(n * (``2` `* n + ``1``) *``         ``(``24` `* n * n * n - ``12` `* n``          ``* n - ``14` `* n + ``7``)) / ``15``;``    ``}` `    ``// Driven Program``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `n = ``4``;``        ` `        ``System.out.println(oddNumSum(n));``    ``}``}` `// This code is contributed by``// Smitha Dinesh Semwal.`

## Python 3

 `# Python 3 Program to find the``# sum of fourth powers of first``# n odd natural numbers` `# calculate the sum of fourth``# power of first n odd natural``#numbers``def` `oddNumSum(n):` `    ``return` `(n ``*` `(``2` `*` `n ``+` `1``) ``*``      ``(``24` `*` `n ``*` `n ``*` `n ``-` `12` `*` `n``      ``*` `n ``-` `14` `*` `n ``+` `7``)) ``/` `15` `# Driven Program``n ``=` `4``print``(``int``(oddNumSum(n)))` `# This code is contributed by``# Smitha Dinesh Semwal.`

## C#

 `// C# Program to find the sum of``// fourth powers of first n``// odd natural numbers``using` `System;` `class` `GFG {` `    ``// calculate the sum of fourth``    ``// power of first n odd``    ``// natural numbers``    ``static` `long` `oddNumSum(``int` `n)``    ``{``        ``return` `(n * (2 * n + 1) *``        ``(24 * n * n * n - 12 * n``        ``* n - 14 * n + 7)) / 15;``    ``}` `    ``// Driven Program``    ``public` `static` `void` `Main()``    ``{``        ``int` `n = 4;``        ``Console.Write(oddNumSum(n));``    ``}``}` `// This code is contributed by``// vt_m.`

## PHP

 ``

## Javascript

 ``

Output:

`  3108`

Time Complexity : O(1)

Space Complexity: O(1)

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