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Find the sum of the first N Centered Octagonal Number
  • Last Updated : 02 Jun, 2020

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:

  1. Initially, we need to create a function which will help us to calculate the Nth centered octagonal numbers.
  2. Now, run a loop starting from 1 to N, to find ith centered octagonal numbers.
  3. Add all the above calculated centered octagonal numbers.
  4. Finally, display the sum of the first N centered octagonal numbers.

Below is the implementation of the above approach:

C++

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// 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

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Java

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// 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

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Python3

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# 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)) 

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C#

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// 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

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Output:

165

Time Complexity: O(N).

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