Sum of square of first n odd numbers
Last Updated :
13 Jun, 2022
Given a number n, find sum of square of first n odd natural numbers.
Examples :
Input : 3
Output : 35
12 + 32 + 52 = 35
Input : 8
Output : 680
12 + 32 + 52 + 72 + 92 + 112 + 132 + 152
A simple solution is to traverse through n odd numbers and find the sum of square.
Below is the implementation of the approach.
C++
#include <iostream>
using namespace std;
int squareSum( int n)
{
int sum = 0;
for ( int i = 1; i <= n; i++)
sum += (2*i - 1) * (2*i - 1);
return sum;
}
int main()
{
cout << squareSum(8);
return 0;
}
|
Java
import java.io.*;
class GFG {
static int squareSum( int n)
{
int sum = 0 ;
for ( int i = 1 ; i <= n; i++)
sum += ( 2 *i - 1 ) * ( 2 *i - 1 );
return sum;
}
public static void main(String args[])
{
System.out.println(squareSum( 8 ));
}
}
|
Python3
def squareSum(n):
sm = 0
for i in range ( 1 , n + 1 ):
sm + = ( 2 * i - 1 ) * ( 2 * i - 1 )
return sm
n = 8
print (squareSum(n))
|
C#
using System;
class GFG {
static int squareSum( int n)
{
int sum = 0;
for ( int i = 1; i <= n; i++)
sum += (2*i - 1) * (2*i - 1);
return sum;
}
public static void Main()
{
Console.Write(squareSum(8));
}
}
|
PHP
<?php
function squareSum( $n )
{
$sum = 0;
for ( $i = 1; $i <= $n ; $i ++)
$sum += (2* $i - 1) * (2* $i - 1);
return $sum ;
}
echo squareSum(8);
?>
|
Javascript
<script>
function squareSum(n)
{
let sum = 0;
for (let i = 1; i <= n; i++)
sum += (2 * i - 1) * (2 * i - 1);
return sum;
}
document.write(squareSum(8));
</script>
|
Output :
680
Time Complexity: O(n), where n represents the given integer.
Auxiliary Space: O(1), no extra space is required, so it is a constant.
An efficient solution is to apply below formula.
sum = n * (4n2 - 1) / 3
How does it work?
Please refer sum of squares of even and odd
numbers for proof.
C++
#include <iostream>
using namespace std;
int squareSum( int n)
{
return n*(4*n*n - 1)/3;
}
int main()
{
cout << squareSum(8);
return 0;
}
|
Java
import java.io.*;
class GFG {
static int squareSum( int n)
{
return n*( 4 *n*n - 1 )/ 3 ;
}
public static void main(String args[])
{
System.out.println(squareSum( 8 ));
}
}
|
Python3
def squareSum( n ):
return int (n * ( 4 * n * n - 1 ) / 3 )
ans = squareSum( 8 )
print (ans)
|
C#
using System;
class GFG {
static int squareSum( int n)
{
return n * (4 * n * n - 1)/3;
}
public static void Main()
{
Console.Write(squareSum(8));
}
}
|
PHP
<?php
function squareSum( $n )
{
return $n * (4 * $n * $n - 1) / 3;
}
echo squareSum(8);
?>
|
Javascript
<script>
function squareSum(n)
{
return n*(4*n*n - 1)/3;
}
document.write(squareSum(8));
</script>
|
Output :
680
Time Complexity: O(1), the code will run in a constant time.
Auxiliary Space: O(1), no extra space is required, so it is a constant.
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