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++

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// 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;
}

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Java

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// 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.

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Python3

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# 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

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C#

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// 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.

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PHP

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<?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
?>

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Output

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


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