Find the sum of the first N Centered Octagonal Number

Last Updated : 01 Dec, 2022

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 N^th centered octagonal numbers.
Now, run a loop starting from 1 to N, to find i^th centered 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# 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

Time Complexity: O(N)
Auxiliary Space: O(1)

Find the sum of the first N Centered Octagonal Number

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Find the sum of the first N Centered Octagonal Number

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