Centered Octadecagonal Number

Given a number n, find the nth Centered Octadecagonal number.

The Centered Octadecagonal Number represents a dot in the centre and others dot are arranged around it in successive layers of octadecagon(18 sided polygon).

center_octadecagon_num

Examples :

Input :  2
Output : 19

Input : 6
Output : 271

In mathmatics, Centered Octadecagonal number for n-th term is given by:

 CO_{n}= 9n^2 -9n+1

Below is the basic implementation of the above idea:

C++

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// C++ Program to find the
// nth centered octadecagonal
// number
#include <bits/stdc++.h>
using namespace std;
  
// centered octadecagon  function
int center_octadecagon_num(long int n)
{
    // Formula to calculate nth
    // centered octadecagonal number
    return 9 * n * n - 9 * n + 1;
}
  
// Driver Code
int main()
{
    long int n = 3;
    cout << n << "th centered octadecagonal number : "
                  << center_octadecagon_num(n);
    cout << endl;
    n = 13;
    cout << n << "th centered octadecagonal number : "
                 << center_octadecagon_num(n);
  
    return 0;
}

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Java

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// Java Program to find the
// nth centered octadecagonal
// number
import java.io.*;
  
class GFG 
{
      
// centered octadecagon function
static int center_octadecagon_num(int n)
{
          
    // Formula to calculate nth
    // centered octadecagonal number
    return 9 * n * n - 9 * n + 1;
}
  
// Driver Code
public static void main (String[] args) 
{
int n = 3;
System.out.print(n + "th centered "
           "octadecagonal number : ");
System.out.println(center_octadecagon_num(n));
  
n = 13;
System.out.print(n + "th centered "
           "octadecagonal number : ");
System.out.println(center_octadecagon_num(n));
}
}
  
// This code is contributed by ajit

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Python3

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# Program to find nth
# centered octadecagonal number
  
# Centered octadecagonal
# number function
def center_octadecagon_num(n) :
      
    # Formula to calculate 
    # nth centered octadecagonal
    # number & return it
    # into main function.
    return(9 * n * n - 
           9 * n + 1)
  
# Driver Code
if __name__ == '__main__' :
          
    n = 3
    print(n,"rd centered octadecagonal " +
                                "number : "
                center_octadecagon_num(n))
  
    n = 13
    print(n,"th centered octadecagonal " +
                              "number : "
                center_octadecagon_num(n))
              
# This code is contributed
# by akt_mit

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C#

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// C# Program to find the
// nth centered octadecagonal
// number
using System;
  
class GFG
{
      
// centered octadecagon function
static int center_octadecagon_num(int n)
{
          
    // Formula to calculate nth
    // centered octadecagonal number
    return 9 * n * n - 9 * n + 1;
}
  
// Driver Code
static public void Main ()
{
      
    int n = 3;
    Console.Write( n + "th centered "
            "octadecagonal number : ");
    Console.WriteLine( center_octadecagon_num(n));
  
    n = 13;
    Console.Write( n + "th centered "
            "octadecagonal number : ");
    Console.WriteLine(center_octadecagon_num(n));
}
}
  
// This code is contributed by aj_36.

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PHP

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<?php
// PHP Program to find the 
// nth centered octadecagonal
// number
  
// centered octadecagon function
function center_octadecagon_num($n)
{
    // Formula to calculate nth
    // centered octadecagonal number
    return (9 * $n * $n
            9 * $n + 1);
}
  
// Driver Code
$n = 3;
echo $n , "th centered octadecagonal "
                            "number : "
             center_octadecagon_num($n);
echo "\n";
  
$n = 13;
echo $n , "th centered octadecagonal "
                            "number : "
             center_octadecagon_num($n);
  
// This code is contributed by m_kit
?>

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Output :

3th centered octadecagonal number : 55
13th centered octadecagonal numbe : 1405


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