Hectagon Number

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

A hectagon number is class of figurate number. It has 100 – sided polygon called hectagon. The N-th hectagon number count’s the 100 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few hectagonol numbers are 1, 100, 297, 592 …

Examples:

Input: N = 2
Output: 100
Explanation:
The second hectagonol number is 100.

Input: N = 3
Output: 297



Approach: The N-th hectagon 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 100 sided polygon is

    Tn =\frac{((100-2)n^2 - (100-4)n)}{2} =\frac{(98n^2 - 96)}{2}

Below is the implementation of the above approach:

C++

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// C++ program for above approach
#include <bits/stdc++.h>
using namespace std;
  
// Finding the nth hectagon Number
int hectagonNum(int n)
{
    return (98 * n * n - 96 * n) / 2;
}
  
// Driver Code
int main()
{
    int n = 3;
    cout << "3rd hectagon Number is = " 
         << hectagonNum(n);
  
    return 0;
}
  
// This code is contributed by shivanisinghss2110

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C

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// C program for above approach
#include <stdio.h>
#include <stdlib.h>
  
// Finding the nth hectagon Number
int hectagonNum(int n)
{
    return (98 * n * n - 96 * n) / 2;
}
  
// Driver program to test above function
int main()
{
    int n = 3;
    printf("3rd hectagon Number is = %d",
           hectagonNum(n));
  
    return 0;
}

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Java

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// Java program for above approach
import java.util.*;
class GFG{
  
// Finding the nth hectagon Number
static int hectagonNum(int n)
{
    return (98 * n * n - 96 * n) / 2;
}
  
// Driver Code
public static void main(String args[])
{
    int n = 3;
    System.out.print("3rd hectagon Number is = " +
                                  hectagonNum(n));
}
}
  
// This code is contributed by Akanksha_Rai

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Python3

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# Python3 program for above approach 
  
# Finding the nth hectagon number 
def hectagonNum(n): 
  
    return (98 * n * n - 96 * n) // 2
  
# Driver code
n = 3
print("3rd hectagon Number is = "
                   hectagonNum(n)) 
  
# This code is contributed by divyamohan123

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C#

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// C# program for above approach
using System;
class GFG{
  
// Finding the nth hectagon Number
static int hectagonNum(int n)
{
    return (98 * n * n - 96 * n) / 2;
}
  
// Driver Code
public static void Main()
{
    int n = 3;
    Console.Write("3rd hectagon Number is = " +
                               hectagonNum(n));
}
}
  
// This code is contributed by Akanksha_Rai

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Output:

3rd hectagon Number is = 297

Reference: https://en.wiktionary.org/wiki/hectagon

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