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Icosagonal number

  • Last Updated : 16 Jul, 2021

Given a number n, the task is to find the nth Icosagonal number. 
An Icosagonal number is the 20-gon is a twenty-sided polygon. The number derived from the figurative class. There are different pattern series number in this number. The dots are countable, arrange in a specific way of position and create a diagram. All the dots have a common dots points, all others dots are connected to this points and except this common point the dots connected to their i-th dots with their respective successive layer.
Examples : 
 

Input : 3 
Output :57
Input :8 
Output :512 
 

 

icosagonal number

Formula for nth icosagonal number: 
 



\begin{math}  Ig_{n}=((18n^2)-16n)/2 \end{math}

 

C++




// C++ program to find
// nth Icosagonal number
#include <bits/stdc++.h>
using namespace std;
 
// Function to calculate Icosagonal number
int icosagonal_poly(long int n)
{
    // Formula for finding
    // nth Icosagonal number
    return (18 * n * n - 16 * n) / 2;
}
 
// Drivers code
int main()
{
    long int n = 7;
    cout << n << "th Icosagonal number :"
               << icosagonal_poly(n);
 
    return 0;
}

Java




// Java program to find
// nth Icosagonal number
 
import java.io.*;
 
class GFG {
     
// Function to calculate Icosagonal number
 
static int icosagonal_poly(int n)
{
    // Formula for finding
    // nth Icosagonal number
    return (18 * n * n - 16 * n) / 2;
}
 
// Drivers code
     
    public static void main (String[] args) {
    
    int n = 7;
     
    System.out.print (n + "th Icosagonal number :");
    System.out.println(icosagonal_poly(n));
    }
}
// This code is contributed by aj_36

Python 3




# Python 3 program to find
# nth Icosagonal number
 
# Function to calculate
# Icosagonal number
def icosagonal_poly(n) :
     
    # Formula for finding
    # nth Icosagonal number
    return (18 * n * n -
            16 * n) // 2
 
# Driver Code
if __name__ == '__main__' :
    n = 7
    print(n,"th Icosagonal number : ",
                   icosagonal_poly(n))
 
# This code is contributed m_kit

C#




// C# program to find
// nth Icosagonal number
using System;
 
class GFG
{
 
// Function to calculate
// Icosagonal number
static int icosagonal_poly(int n)
{
    // Formula for finding
    // nth Icosagonal number
    return (18 * n * n -
            16 * n) / 2;
}
 
// Driver code
static public void Main ()
{
     
int n = 7;
 
Console.Write(n + "th Icosagonal " +
                        "number :");
Console.WriteLine(icosagonal_poly(n));
}
}
 
// This code is contributed by ajit

PHP




<?php
// PHP program to find
// nth Icosagonal number
 
// Function to calculate
// Icosagonal number
function icosagonal_poly($n)
{
    // Formula for finding
    // nth Icosagonal number
    return (18 * $n *
            $n - 16 * $n) / 2;
}
 
// Driver Code
$n = 7;
echo $n , "th Icosagonal number :",
               icosagonal_poly($n);
 
// This code is contributed by ajit
?>

Javascript




<script>
    // Javascript program to find nth Icosagonal number
     
    // Function to calculate
    // Icosagonal number
    function icosagonal_poly(n)
    {
        // Formula for finding
        // nth Icosagonal number
        return (18 * n * n - 16 * n) / 2;
    }
     
    let n = 7;
   
    document.write(n + "th Icosagonal number :");
    document.write(icosagonal_poly(n));
     
</script>

Output : 
 

7th Icosagonal number :385

Time Complexity: O(1)
Auxiliary Space: O(1)

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

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