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Hexadecagonal number

  • Last Updated : 06 Sep, 2021

Given a number n, the task is to find the nth hexadecagonal number. 
A Hexadecagonal number is class of figurate number and a perfect squares. It has sixteen sided polygon called hexadecagon or hexakaidecagon. The n-th hexadecagonal number count’s the sixteen number of dots and all others dots are surrounding to its successive layer. 
Examples : 
 

Input : 2 
Output :16
Input :7 
Output :301 
 

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Formula to calculate hexadecagonal number:

  \begin{math}  Hg_{n}=(14n^2-12n)/2 \end{math}  

C++




// C++ program to find Nth
// hexadecagon number
#include <bits/stdc++.h>
using namespace std;
  
// Function to calculate hexadecagonal number
int hexadecagonalNum(long int n)
{
    return ((14 * n * n) - 12 * n) / 2;
}
  
// Drivers Code
int main()
{
    long int n = 5;
    cout << n << "th Hexadecagonal number : ";
    cout << hexadecagonalNum(n);
    cout << endl;
    n = 9;
    cout << n << "th Hexadecagonal number : ";
    cout << hexadecagonalNum(n);
  
    return 0;
}

Java




// Java program to find Nth hexadecagon
// number
import java.io.*;
  
class GFG {
  
    // Function to calculate hexadecagonal
    // number
    static long hexadecagonalNum(long n)
    {
        return ((14 * n * n) - 12 * n) / 2;
    }
      
    // Drivers Code
    public static void main (String[] args)
    {
        long n = 5;
        System.out.println( n + "th "
          + "Hexadecagonal number : "
              + hexadecagonalNum(n));
                
        n = 9;
        System.out.println( n + "th "
          + "Hexadecagonal number : "
              + hexadecagonalNum(n));
    }
}
  
// This code contributed by anuj_67.

Python3




# Python program to find Nth
# hexadecagon number
  
# Function to calculate
# hexadecagonal number
def hexadecagonalNum(n):
  
    # Formula to calculate nth
    # Centered hexadecagonal number
    return ((14 * n * n) - 12 * n) // 2
  
# Driver Code
n = 5
print("%sth Hexadecagonal number : " %n,
                    hexadecagonalNum(n))
n = 9
print("%sth Hexadecagonal number : " %n,
                    hexadecagonalNum(n))
                      
# This code is contributed by ajit                 

C#




// C# program to find Nth hexadecagon
// number
using System;
class GFG {
  
    // Function to calculate hexadecagonal
    // number
    static long hexadecagonalNum(long n)
    {
        return ((14 * n * n) - 12 * n) / 2;
    }
      
    // Drivers Code
    public static void Main ()
    {
        long n = 5;
        Console.WriteLine( n + "th "
        + "Hexadecagonal number : "
            + hexadecagonalNum(n));
              
        n = 9;
        Console.WriteLine( n + "th "
        + "Hexadecagonal number : "
            + hexadecagonalNum(n));
    }
}
  
// This code contributed by anuj_67.

PHP




<?php
// PHP program to find Nth
// hexadecagon number
  
// Function to calculate 
// hexadecagonal number
  
function hexadecagonalNum($n)
{
    return ((14 * $n * $n) - 12 * $n) / 2;
}
  
// Driver Code
$n = 5;
echo $n , "th Hexadecagonal number : ";
echo hexadecagonalNum($n);
echo "\n";
  
$n = 9;
echo $n , "th Hexadecagonal number : ";
echo hexadecagonalNum($n);
  
// This code is contributed bu m_kit
?>

Javascript




<script>
  
// Javascript program to find Nth hexadecagon
// number
  
// Function to calculate hexadecagonal
// number
function hexadecagonalNum(n)
{
    return ((14 * n * n) - 12 * n) / 2;
}
  
// Driver code
var n = 5;
document.write(n + "th "
               "Hexadecagonal number : " +
               hexadecagonalNum(n) + "<br>");
    
n = 9;
document.write(n + "th "
               "Hexadecagonal number : "
               hexadecagonalNum(n));
  
// This code is contributed by Khushboogoyal499
  
</script>

Output : 
 

5th Hexadecagonal number : 145
9th Hexadecagonal number : 513

Time Complexity: O(1)
Auxiliary Space: O(1)
Reference: https://en.wikipedia.org/wiki/Polygonal_number
 




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