Icosidigonal number

Given a number n, the task is to find the nth Icosidigonal number (Isdn).
The polygon has the many gons, depends on their gonal number series. In mathematics, there is a number of gonal numbers and the icosidigonal number is one of them and these numbers have 22 -sided polygon (icosidigon). An icosidigonal number belong to the class of figurative number. They have one common dots points and other dots pattern is arranged in an n-th nested icosidigon pattern.

Examples :

Input : 2
Output :22

Input :6
Output :306

icosidigonal number22

Formula for nth Icosidigonal number:

  \begin{math}  Isd_{n}=((20n^2)-18n)/2 \end{math}  

C++

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// C++ program to find nth Icosidigonal
// number
#include <bits/stdc++.h>
using namespace std;
  
// Function to calculate Icosidigonal number
int icosidigonal_num(long int n)
{
    // Formula for finding
    // nth Icosidigonal number
    return (20 * n * n - 18 * n) / 2;
}
  
// Driver function
int main()
{
    long int n = 4;
    cout << n << "th Icosidigonal number :" << icosidigonal_num(n);
    cout << endl;
    n = 8;
    cout << n << "th Icosidigonal number:" << icosidigonal_num(n);
    return 0;
}

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Java

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// Java program to find nth 
// Icosidigonal number 
import java.io.*;
  
class GFG 
{
      
    // Function to calculate 
    // Icosidigonal number
    static int icosidigonal_num(int n) 
    {
          
    // Formula for finding
    // nth Icosidigonal number
      
    return (20 * n * n - 18 * n) / 2;
    }
  
// Driver Code
public static void main (String[] args) 
{
  
    int n = 4;
    System.out.print (n + "th Icosidigonal number :");
    System.out.println (icosidigonal_num(n));
  
    n = 8;
    System.out.print (n + "th Icosidigonal number :");
    System.out.println (icosidigonal_num(n));
}
}
  
// This code is contributed by ajit

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Python 3

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# python 3 program to find 
# nth Icosidigonal number
  
# Function to calculate
# Icosidigonal number
def icosidigonal_num(n) :
      
    # Formula for finding
    # nth Icosidigonal number
    return (20 * n * n - 
            18 * n) // 2
  
# Driver Code
if __name__ == '__main__' :
          
    n = 4
    print(n,"th Icosidigonal " +
                    "number : "
            icosidigonal_num(n))
    n = 8
    print(n,"th Icosidigonal " +
                    "number : "
            icosidigonal_num(n))
      
# This code is contributed m_kit

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C#

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// C# program to find nth 
// Icosidigonal number 
using System;
  
class GFG
{
      
    // Function to calculate 
    // Icosidigonal number
    static int icosidigonal_num(int n) 
    {
          
    // Formula for finding
    // nth Icosidigonal number
    return (20 * n * n - 
            18 * n) / 2;
    }
  
// Driver Code
static public void Main ()
{
int n = 4;
Console.Write(n + "th Icosidigonal " +
                          "number :");
Console.WriteLine(icosidigonal_num(n));
  
n = 8;
Console.Write (n + "th Icosidigonal "+
                          "number :");
Console.WriteLine(icosidigonal_num(n));
}
}
  
// This code is contributed by ajit

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PHP

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<?php
// PHP program to find nth
// Icosidigonal number
  
// Function to calculate
// Icosidigonal number
function icosidigonal_num($n)
{
    // Formula for finding
    // nth Icosidigonal number
    return (20 * $n * $n - 18 * $n) / 2;
}
  
// Driver Code
$n = 4;
echo $n , "th Icosidigonal number : ",
                icosidigonal_num($n);
echo "\n";
$n = 8;
echo $n , "th Icosidigonal number : ",
               icosidigonal_num($n);
      
// This code is contributed by m_kit
?>

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Output :

4th Icosidigonal number :124
8th Icosidigonal number:568

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



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