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Hexacontagon Number

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  • Last Updated : 23 Jun, 2021
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Given a number N, the task is to find Nth Hexacontagon number
 

A Hexacontagon number is class of figurate number. It has 60 – sided polygon called hexacontagon. The N-th hexacontagon number count’s the 60 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few hexacontagonol numbers are 1, 60, 177, 352 … 
 

Examples: 
 

Input: N = 2 
Output: 60 
Explanation: 
The second hexacontagonol number is 60. 
Input: N = 3 
Output: 177 
 

 

Approach: The N-th hexacontagon 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 60 sided polygon is
     

Tn =\frac{((60-2)n^2 - (60-4)n)}{2} =\frac{(58n^2 - 56)}{2}

  •  

Below is the implementation of the above approach: 
 

C++




// C++ program for above approach
#include <iostream>
using namespace std;
 
// Finding the nth hexacontagon number
int hexacontagonNum(int n)
{
    return (58 * n * n - 56 * n) / 2;
}
 
// Driver code
int main()
{
    int n = 3;
    cout << "3rd hexacontagon Number is = "
         << hexacontagonNum(n);
 
    return 0;
}
 
// This code is contributed by shubhamsingh10


C




// C program for above approach
#include <stdio.h>
#include <stdlib.h>
 
// Finding the nth hexacontagon Number
int hexacontagonNum(int n)
{
    return (58 * n * n - 56 * n) / 2;
}
 
// Driver program to test above function
int main()
{
    int n = 3;
    printf("3rd hexacontagon Number is = %d",
           hexacontagonNum(n));
 
    return 0;
}


Java




// Java program for above approach
class GFG{
     
// Finding the nth hexacontagon number
public static int hexacontagonNum(int n)
{
    return (58 * n * n - 56 * n) / 2;
}
 
// Driver code
public static void main(String[] args)
{
    int n = 3;
    System.out.println("3rd hexacontagon Number is = " +
                                    hexacontagonNum(n));
}
}
 
// This code is contributed by divyeshrabadiya07   


Python3




# Python3 program for above approach
 
# Finding the nth hexacontagon Number
def hexacontagonNum(n):
 
    return (58 * n * n - 56 * n) // 2
 
# Driver Code
n = 3
print("3rd hexacontagon Number is = ",
                  hexacontagonNum(n));
 
# This code is contributed by divyamohan123


C#




// C# program for above approach
using System;
 
class GFG{
     
// Finding the nth hexacontagon number
public static int hexacontagonNum(int n)
{
    return (58 * n * n - 56 * n) / 2;
}
 
// Driver code
public static void Main()
{
    int n = 3;
    Console.Write("3rd hexacontagon Number is = " +
                               hexacontagonNum(n));
}
}
 
// This code is contributed by Code_Mech


Javascript




<script>
 
 
// Javascript program for above approach
 
// Finding the nth hexacontagon number
function hexacontagonNum(n)
{
    return (58 * n * n - 56 * n) / 2;
}
 
// Driver code
var n = 3;
document.write("3rd hexacontagon Number is = " +hexacontagonNum(n));
 
 
</script>


Output: 

3rd hexacontagon Number is = 177

 

Time Complexity: O(1)

Auxiliary Space: O(1)

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

 


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