Hendecagonal number

Given a number n, the task is to find the nth Hendecagonal number.
A Hendecagonal number is a figurate number that extends the concept of triangular and square numbers to the decagon (Eleven -sided polygon). The nth hendecagonal number counts the number of dots in a pattern of n nested decagons, all sharing a common corner, where the ith hendecagon in the pattern has sides made of i dots spaced one unit apart from each other.

Examples:

Input : 2
Output :11



Input :6
Output :141

img

Formula for nth hendecagonal number :

  \begin{math}  H_{n}=((9n^2)-7n)/2 \end{math}  

C++

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// C++ program to find nth
// Hendecagonal number
#include <bits/stdc++.h>
using namespace std;
  
// Function to find
// Hendecagonal number
int hendecagonal_num(int n)
{
    // Formula to calculate nth
    // Hendecagonal number
    return (9 * n * n - 7 * n) / 2;
}
  
// Driver Code
int main()
{
    int n = 3;
    cout << n << "rd Hendecagonal number: ";
    cout << hendecagonal_num(n);
    cout << endl;
    n = 10;
    cout << n << "th Hendecagonal number: ";
    cout << hendecagonal_num(n);
  
    return 0;
}

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Java

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// Java program to find nth
// Hendecagonal number
import java.io.*;
  
class GFG
{
      
// Function to find
// Hendecagonal number
static int hendecagonal_num(int n)
{
    // Formula to calculate nth
    // Hendecagonal number
    return (9 * n * n - 
            7 * n) / 2;
}
  
// Driver Code
public static void main (String[] args)
{
int n = 3;
System.out.print(n + "rd Hendecagonal " +
                             "number: ");
System.out.println(hendecagonal_num(n));
  
n = 10;
System.out.print(n + "th Hendecagonal "
                             "number: ");
System.out.println(hendecagonal_num(n));
}
}
  
// This code is contributed by ajit

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Python3

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# Program to find nth
# Hendecagonal number
  
# Function of Hendecagonal 
# number 
def hendecagonal_num(n) :
      
    # Formula to calculate nth
    # Hendecagonal number &
    # return it into main function.
      
    return (9 * n * n -
            7 * n) // 2
  
# Driver Code
if __name__ == '__main__' :
          
    n = 3
    print(n,"rd Hendecagonal number : "
                    hendecagonal_num(n))
  
    n = 10
    print(n,"th Hendecagonal number : "
                    hendecagonal_num(n))
  
# This code is contributed by ajit

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C#

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// C# program to find nth
// Hendecagonal number
using System;
  
class GFG
{
// Function to find
// Hendecagonal number
static int hendecagonal_num(int n)
{
    // Formula to calculate nth
    // Hendecagonal number
    return (9 * n * n - 7 * n) / 2;
}
  
// Driver Code
static public void Main ()
{
    int n = 3;
    Console.Write(n + 
                 "rd Hendecagonal number: ");
    Console.WriteLine( hendecagonal_num(n));
  
    n = 10;
    Console.Write(n + 
                 "th Hendecagonal number: ");
    Console.WriteLine( hendecagonal_num(n));
    }
}
  
// This code is contributed by aj_36

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PHP

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<?php
// PHP program to find nth
// Hendecagonal number
  
// Function to find
// Hendecagonal number
  
function hendecagonal_num($n)
{
      
    // Formula to calculate nth
    // Hendecagonal number
    return (9 * $n * $n - 7 * $n) / 2;
}
  
// Driver Code
$n = 3;
echo $n , "th Hendecagonal number: ";
echo hendecagonal_num($n);
echo "\n";
      
$n = 10;
echo $n , "th Hendecagonal number: ";
echo hendecagonal_num($n);
  
// This code is contributed by m_kit
?>

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Output :

3th Hendecagonal number: 30
10th Hendecagonal number: 415

Reference: https://en.wikipedia.org/wiki/Polygonal_number



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