# Sum of fourth powers of first n odd natural numbers

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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Naive Approach :- In this Simple finding the fourth powers of the first n odd natural numbers is iterate a loop from 1 to n time, 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

 ` `

Output:

```24310
```

Time Complexity : O(N)

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

 ` `

Output:

```  3108
```

Time Complexity : O(1)

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