# Sum of square of first n odd numbers

The series of squares of first n odd numbers takes squares of of first n odd numbers in series.

The series is: 1,9,25,49,81,121…

The series can also be written as − 12, 32, 52, 72, 92, 112….

The sum of this series has a mathematical formula −

n(2n+1)(2n-1)/ 3= n(4n2 - 1)/3

Lets take an example,

Input: N = 4
Output: sum =

## Explanation

12 + 32 + 52 + 72 = 1 +9+ 25 + 49 = 84

Using formula, sum = 4(4(4)2- 1)/3 = 4(64-1)/3 = 4(63)/3 = 4*21 = 84 both these methods are good but the one using mathematical formula is better because it does not use looks which reduces its time complexity.

## Example

#include <stdio.h>
int main() {
int n = 8;
int sum = 0;
for (int i = 1; i <= n; i++)
sum += (2*i - 1) * (2*i - 1);
printf("The sum of square of first %d odd numbers is %d",n, sum);
return 0;
}

## Output

The sum of square of first 8 odd numbers is 680

## Example

#include <stdio.h>
int main() {
int n = 18;
int sum = ((n*((4*n*n)-1))/3);
printf("The sum of square of first %d odd numbers is %d",n, sum);
return 0;
}

## Output

The sum of square of first 18 odd numbers is 7770