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Enneacontahexagon numbers

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Given a number N, the task is to find Nth Enneacontahexagon number.
 

An Enneacontahexagon number is a class of figurate numbers. It has a 96-sided polygon called Enneacontahexagon. The N-th Enneacontahexagon number count’s the 96 number of dots and all other dots are surrounding with a common sharing corner and make a pattern. The first few Enneacontahexagonol numbers are 1, 96, 285, 568, 945, 1416, … 
 


Examples: 
 

Input: N = 2 
Output: 96 
Explanation: 
The second Enneacontahexagonol number is 96. 
Input: N = 3 
Output: 285 
 


 


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

  • Nth term of s sided polygon = \frac{((s-2)n^2 - (s-4)n)}{2}
     
  • Therefore Nth term of 96 sided polygon is
     

Tn =\frac{((96-2)n^2 - (96-4)n)}{2} =\frac{(94^2 - 92)}{2}
 

Below is the implementation of the above approach:

C++

// C++ implementation for
// above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the Nth
// Enneacontahexagon Number
int EnneacontahexagonNum(int n)
{
    return (94 * n * n - 92 * n) / 2;
}
 
// Driver Code
int main()
{
    int n = 3;
    cout << EnneacontahexagonNum(n);
 
    return 0;
}

                    

Java

// Java program to find N-th
// Enneacontahexagon Number
class GFG{
 
// Function to find the nth
// Enneacontahexagon Number
static int enneacontahexagonNum(int n)
{
    return (94 * n * n - 92 * n) / 2;
}
 
// Driver code
public static void main(String[] args)
{
    int n = 3;
    System.out.print(enneacontahexagonNum(n));
}
}
 
// This code is contributed by shubham

                    

Python3

# Python3 implementation for
# above approach
 
# Function to find the Nth
# Enneacontahexagon Number
def EnneacontahexagonNum(n):
 
    return (94 * n * n - 92 * n) // 2;
 
# Driver Code
n = 3;
print(EnneacontahexagonNum(n));
 
# This code is contributed by Code_Mech

                    

C#

// C# program to find N-th
// Enneacontahexagon Number
using System;
class GFG{
 
// Function to find the nth
// Enneacontahexagon Number
static int enneacontahexagonNum(int n)
{
    return (94 * n * n - 92 * n) / 2;
}
 
// Driver code
public static void Main()
{
    int n = 3;
    Console.Write(enneacontahexagonNum(n));
}
}
 
// This code is contributed by Code_Mech

                    

Javascript

<script>
 
// Javascript program to find N-th
// Enneacontahexagon Number
 
 
    // Function to find the nth
    // Enneacontahexagon Number
    function EnneacontahexagonNum( n) {
        return (94 * n * n - 92 * n) / 2;
    }
 
    // Driver code
      
        let n = 3;
        document.write(EnneacontahexagonNum(n));
 
 
// This code contributed by aashish1995
 
</script>

                    

Output: 
285

 

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


 



Last Updated : 23 Mar, 2021
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