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 
 

Formula for nth hendecagonal number : 
 

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

// 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;
}

// C program to find nth
// Hendecagonal number
#include <stdio.h>

// 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;
    printf("%drd Hendecagonal number: ",n);
    printf("%d\n",hendecagonal_num(n));

    n = 10;
    printf("%dth Hendecagonal number: ",n);
    printf("%d\n",hendecagonal_num(n));

    return 0;
}

// This code is contributed by kothavvsaakash.

// 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

# 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

// 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

<?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
?>

<script>
    // Javascript 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;
    }
    
    let n = 3;
    document.write(n + "rd Hendecagonal number: ");
    document.write(hendecagonal_num(n) + "</br>");
    n = 10;
    document.write(n + "th Hendecagonal number: ");
    document.write(hendecagonal_num(n));

// This code is contributed by divyesh072019.
</script>

Output : 
 

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

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