Hexacontatetragon numbers

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

An Hexacontatetragon number is a class of figurate numbers. It has a 64-sided polygon called Hexacontatetragon. The N-th Hexacontatetragon number count’s the 64 number of dots and all other dots are surrounding with a common sharing corner and make a pattern. The first few Hexacontatetragonol numbers are 1, 64, 189, 376, 625, 936, …

Examples:

Input: N = 2
Output: 64
Explanation:
The second Hexacontatetragonol number is 64.

Input: N = 3
Output: 189



Approach: The N-th Hexacontatetragon 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 64 sided polygon is

    Tn =\frac{((64-2)n^2 - (64-4)n)}{2} =\frac{(62^2 - 60)}{2}

Below is the implementation of the above approach:

C++

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// C++ implementation for above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to Find the 
// Nth Hexacontatetragon Number
int HexacontatetragonNum(int n)
{
    return (62 * n * n - 60 * n) / 2;
}
  
// Driver Code
int main()
{
    int n = 3;
    cout << HexacontatetragonNum(n);
  
    return 0;
}

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Java

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// Java program to find N-th 
// Hexacontatetragon number 
class GFG{ 
  
// Function to find the nth 
// Hexacontatetragon number 
static int HexacontatetragonNum(int n) 
    return (62 * n * n - 60 * n) / 2;
  
// Driver code 
public static void main(String[] args) 
    int n = 3
    System.out.print(HexacontatetragonNum(n)); 
  
// This code is contributed by shubham 

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Python3

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# Python3 implementation for above approach
  
# Function to Find the 
# Nth Hexacontatetragon Number
def HexacontatetragonNum(n):
  
    return (62 * n * n - 60 * n) / 2;
  
# Driver Code
n = 3;
print(HexacontatetragonNum(n));
  
# This code is contributed by Code_Mech

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C#

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// C# program to find N-th 
// Hexacontatetragon number 
using System;
class GFG{ 
  
// Function to find the nth 
// Hexacontatetragon number 
static int HexacontatetragonNum(int n) 
    return (62 * n * n - 60 * n) / 2;
  
// Driver code 
public static void Main() 
    int n = 3; 
    Console.Write(HexacontatetragonNum(n)); 
  
// This code is contributed by Code_Mech

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Output:

189

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

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