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Find the sum of the first N Centered Octagonal Number

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  • Last Updated : 17 Mar, 2021

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++




// 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).
 


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