The sum of the squares of the first n odd numbers

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

The series is: 1,9,25,49,81,121…

The series can also be written as- 1², 3² , 5², 7², 9 ², 11²….

The sum of this series is A mathematical formula-

n(2n 1) (2n-1)/ 3= n(4n² - 1)/3

For example,

Input: N = 4
Output: sum =

Explanation

12 3² 5² 7² = 1 9 25 49 = 84

Using the formula, sum = 4(4(4)²- 1)/3 = 4(64-1)/3 = 4(63)/3 = 4*21 = 84 Both methods is good, but the method using mathematical formulas is better because it doesn't use looks, thus reducing the 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

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