Given a number N, the task is to find the sum of the first N Centered Octagonal Numbers.
The first few Centered Octagonal numbers are 1, 9, 25, 49, 81, 121, 169, 225, 289, 361 …
Examples:
Input: N = 3
Output: 35
Explanation:
1, 9 and 25 are the first three Centered Octagonal numbers.Input: N = 5
Output: 165
Approach:
- Initially, we need to create a function that will help us to calculate the Nthcentered octagonal numbers.
- Now, run a loop starting from 1 to N, to find ithcentered octagonal numbers.
- Add all the above calculated centered octagonal numbers.
- Finally, display the sum of the first N-centered octagonal numbers.
Below is the implementation of the above approach:
C++
// C++ program to find the sum of the // first N centered octagonal number #include<bits/stdc++.h> using namespace std;
// Function to find the N-th centered // octagonal number int center_Octagonal_num( int n)
{ // Formula to calculate
// nth centered octagonal
// number
return (4 * n * n - 4 * n + 1);
} // Function to find the sum of the first // N centered octagonal numbers int sum_center_Octagonal_num( int n)
{ // Variable to store
// the sum
int summ = 0;
// Iterating through the range
// 1 to N
for ( int i = 1; i < n + 1; i++)
{
summ += center_Octagonal_num(i);
}
return summ;
} // Driver Code int main()
{ int n = 5;
cout << (sum_center_Octagonal_num(n));
return 0;
} // This code is contributed by PratikBasu |
Java
// Java program to find the sum of the // first N centered octagonal number class GFG {
// Function to find N-th centered // octagonal number static int center_Octagonal_num( int n)
{ // Formula to calculate
// nth centered octagonal
// number
return ( 4 * n * n - 4 * n + 1 );
} // Function to find the // sum of the first N // centered octagonal // numbers static int sum_center_Octagonal_num( int n)
{ // Variable to store
// the sum
int summ = 0 ;
// Iterating through the first N
// numbers
for ( int i = 1 ; i < n + 1 ; i++)
{
summ += center_Octagonal_num(i);
}
return summ;
} // Driver code public static void main(String[] args)
{ int n = 5 ;
System.out.println(sum_center_Octagonal_num(n));
} } // This code is contributed by Princi Singh |
Python3
# Python3 program to find the # sum of the first N # Centered Octagonal number # Function to find N-th # Centered Octagonal # number def center_Octagonal_num(n):
# Formula to calculate
# nth centered Octagonal
# number
return ( 4 * n * n - 4 * n + 1 )
# Function to find the # sum of the first N # Centered Octagonal # numbers def sum_center_Octagonal_num(n) :
# Variable to store
# the sum
summ = 0
# Iterating through the first N
# numbers
for i in range ( 1 , n + 1 ):
summ + = center_Octagonal_num(i)
return summ
# Driver code if __name__ = = '__main__' :
n = 5
print (sum_center_Octagonal_num(n))
|
C#
// C# program to find the sum of the // first N centered octagonal number using System;
class GFG{
// Function to find N-th centered // octagonal number static int center_Octagonal_num( int n)
{ // Formula to calculate
// nth centered octagonal
// number
return (4 * n * n - 4 * n + 1);
} // Function to find the sum of // the first N centered octagonal // numbers static int sum_center_Octagonal_num( int n)
{ // Variable to store
// the sum
int summ = 0;
// Iterating through the first N
// numbers
for ( int i = 1; i < n + 1; i++)
{
summ += center_Octagonal_num(i);
}
return summ;
} // Driver code public static void Main()
{ int n = 5;
Console.WriteLine(sum_center_Octagonal_num(n));
} } // This code is contributed by Akanksha_Rai |
Javascript
<script> // Javascript program to find the sum of the
// first N centered octagonal number
// Function to find the N-th centered
// octagonal number
function center_Octagonal_num(n)
{
// Formula to calculate
// nth centered octagonal
// number
return (4 * n * n - 4 * n + 1);
}
// Function to find the sum of the first
// N centered octagonal numbers
function sum_center_Octagonal_num(n)
{
// Variable to store
// the sum
let summ = 0;
// Iterating through the range
// 1 to N
for (let i = 1; i < n + 1; i++)
{
summ += center_Octagonal_num(i);
}
return summ;
}
let n = 5;
document.write(sum_center_Octagonal_num(n));
</script> // This code is contributed by divyeshrabadiya07. |
Output
165
Time Complexity: O(N)
Auxiliary Space: O(1)
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