Tetracontadigonal Number

Given a number N, the task is to find N^th Tetracontadigon number.

A Tetracontadigon number is a class of figurate numbers. It has a 42-sided polygon called Tetracontadigon. The N-th Tetracontadigonal number count’s the 42 number of dots and all other dots are surrounding with a common sharing corner and make a pattern. The first few Tetracontadigonol numbers are 1, 42, 123, 244, 405, 606 …

Examples:

Input: N = 2 
Output: 42 
Explanation:
The second Tetracontadigonol number is 42. 
Input: N = 3 
Output: 123 

Approach: The N-th Tetracontadigonal number is given by the formula:

• Nth term of s sided polygon = 
  
• Therefore Nth term of 42 sided polygon is
  

• 
  

Below is the implementation of the above approach:

C++

// C++ implementation for the
// above approach
#include <bits/stdc++.h>
using namespace std;

// Function to find the
// nth Tetracontadigonal Number
int TetracontadigonalNum(int n)
{
    return (40 * n * n - 38 * n) / 2;
}

// Driver Code
int main()
{
    int n = 3;
    cout << TetracontadigonalNum(n);

    return 0;
}

Java

// Java implementation for the
// above approach
import java.util.*;
class GFG{

// Function to find the
// nth Tetracontadigonal Number
static int TetracontadigonalNum(int n)
{
    return (40 * n * n - 38 * n) / 2;
}

// Driver Code
public static void main(String[] args)
{
    int n = 3;
    System.out.print(TetracontadigonalNum(n));
}
}

// This code is contributed by Rajput-Ji

Python3

# Python3 implementation for the
# above approach

# Function to find the
# nth tetracontadigonal number
def TetracontadigonalNum(n):

    return int((40 * n * n - 38 * n) / 2)

# Driver Code
n = 3
print (TetracontadigonalNum(n))

# This code is contributed by PratikBasu

C#

// C# implementation for the
// above approach
using System;
class GFG{

// Function to find the
// nth Tetracontadigonal Number
static int TetracontadigonalNum(int n)
{
    return (40 * n * n - 38 * n) / 2;
}

// Driver Code
public static void Main()
{
    int n = 3;
    Console.Write(TetracontadigonalNum(n));
}
}

// This code is contributed by Code_Mech

Javascript

<script>
// Javascript implementation for the
// above approach


    // Function to find the
    // nth Tetracontadigonal Number
    function TetracontadigonalNum( n) {
        return (40 * n * n - 38 * n) / 2;
    }

    // Driver Code

        let n = 3;
        document.write(TetracontadigonalNum(n));

// This code is contributed by todaysgaurav

</script>

Output:

123

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