Centered Octagonal Number

Given a number n, find the nth centered octagonal number.

A centered octagonal number represents an octagon with a dot in the centre and others dots surrounding the centre dot in the successive octagonal layer.

Examples :

Input :  2
Output : 9

Input : 5
Output : 81

Centered Octagonal n-th Number is given by :

CO_{n}= 4n^2 -4n+1

Basic Implementation of the above approach:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// Program to find nth
// centered octagonal 
// number
#include <bits/stdc++.h>
using namespace std;
  
// Centered octagonal number function
int cen_octagonalnum(long int n)
{
    // Formula to calculate nth
    // centered octagonal number &
    // return it into main function.
    return (4 * n * n - 4 * n + 1);
}
  
// Driver Code
int main()
{
    long int n = 6;
    cout << n << "th  centered" 
                 << " octagonal number : ";
    cout << cen_octagonalnum(n);
    cout << endl;
    n = 11;
    cout << n << "th  centered"
                  << " octagonal number : ";
    cout << cen_octagonalnum(n);
  
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java Program to find nth
// centered octagonal number
import java.io.*;
   
class GFG 
{
       
    // Function to find centered
    // octagonal number
    static int centeredoctagonalNumber(int n)
    {
        // Formula to calculate nth 
        // centered octagonal number
        // and return it into main function
        return 4 * n * (n - 1) + 1;
    }
       
    // Driver Code
    public static void main(String args[])
    {
        int n = 6;
        System.out.print(n + "th centered " +
                       "octagonal number: ");
        System.out.println(
                 centeredoctagonalNumber(n));
          
        n = 11;
        System.out.print(n + "th centered " +
                       "octagonal number: ");
        System.out.println(
                  centeredoctagonalNumber(n));
           
    }
}
  
// This code has been contributed by Prasad_Kshirsagar.

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Program to find nth 
# centered octagonal number
  
def cen_octagonalnum(n) :
      
    # Formula to calculate nth
    # centered octagonal number
    return (4 * n * n -
            4 * n + 1)
  
# Driver Code
if __name__ == '__main__' :
          
    n = 6
    print(n,"th Centered"
            "octagonal number: ",
             cen_octagonalnum(n))
    n = 11
    print(n,"th Centered" ,
            "octagonal number: ",
             cen_octagonalnum(n))
                  
# This code is contributed
# by akt_mit

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// Program to find nth centered octagonal 
// number
using System;
  
public class GFG{
      
    // Centered octagonal number function
    static long cen_octagonalnum(long  n)
    {
          
        // Formula to calculate nth
        // centered octagonal number &
        // return it into main function.
        return (4 * n * n - 4 * n + 1);
    }
      
    // Driver code
    static public void Main ()
    {
        long n = 6;
        Console.WriteLine(n + "th centered"
                    + " octagonal number : "
        + cen_octagonalnum(n));
      
        n = 11;
        Console.WriteLine(n + "th centered"
                    + " octagonal number : "
                    + cen_octagonalnum(n));
    }
}
  
// This code is contributed by anuj_67.

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// Program to find nth
// centered octagonal 
// number
  
// Centered octagonal
// number function
function cen_octagonalnum($n)
{
    // Formula to calculate nth
    // centered octagonal number &
    // return it into main function.
    return (4 * $n * $n
            4 * $n + 1);
}
  
// Driver Code
$n = 6;
echo $n ,"th centered",
     " octagonal number : ";
echo cen_octagonalnum($n);
echo "\n";
  
$n = 11;
echo $n , "th centered",
     " octagonal number : ";
echo cen_octagonalnum($n);
  
  
// This code is contributed by ajit
?>

chevron_right



Output

6th  centered octagonal number : 121
11th  centered octagonal number : 441


My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : vt_m, jit_t