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Heptacontagon Number

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  • Last Updated : 23 Jun, 2021

Given a number N, the task is to find Nth Heptacontagon number
 

A Heptacontagon number is class of figurate number. It has 70 – sided polygon called heptacontagon. The N-th heptacontagon number count’s the 70 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few heptacontagonol numbers are 1, 70, 207, 412 … 
 

Examples: 
 

Input: N = 2 
Output: 70 
Explanation: 
The second heptacontagonol number is 70. 
Input: N = 3 
Output: 207 
 

 

Approach: The N-th heptacontagon 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 70 sided polygon is
     

Tn =\frac{((70-2)n^2 - (70-4)n)}{2} =\frac{(68n^2 - 66)}{2}

  •  

Below is the implementation of the above approach: 
 

C++




// C++ program for above approach
#include <bits/stdc++.h>
using namespace std;
 
// Finding the nth heptacontagon number
int heptacontagonNum(int n)
{
    return (68 * n * n - 66 * n) / 2;
}
 
// Driver code
int main()
{
    int N = 3;
     
    cout << "3rd heptacontagon Number is = "
         << heptacontagonNum(N);
 
    return 0;
}
 
// This code is contributed by shivanisinghss2110

C




// C program for above approach
#include <stdio.h>
#include <stdlib.h>
 
// Finding the nth heptacontagon Number
int heptacontagonNum(int n)
{
    return (68 * n * n - 66 * n) / 2;
}
 
// Driver code
int main()
{
    int N = 3;
    printf("3rd heptacontagon Number is = %d",
           heptacontagonNum(N));
 
    return 0;
}

Java




// Java program for the above approach
class GFG{
 
// Finding the nth heptacontagon number
static int heptacontagonNum(int n)
{
    return (68 * n * n - 66 * n) / 2;
}
 
// Driver Code
public static void main(String[] args)
{
    int N = 3;
    System.out.println("3rd heptacontagon Number is = " +
                                    heptacontagonNum(N));
}
}
 
// This code is contributed by rutvik_56

Python3




# Python3 program for above approach
 
# Finding the nth heptacontagon Number
def heptacontagonNum(n):
 
    return (68 * n * n - 66 * n) // 2;
 
# Driver code
N = 3;
print("3rd heptacontagon Number is =",
                 heptacontagonNum(N));
 
# This code is contributed by Akanksha_Rai

C#




// C# program for the above approach
using System;
class GFG{
 
// Finding the nth heptacontagon number
static int heptacontagonNum(int n)
{
    return (68 * n * n - 66 * n) / 2;
}
 
// Driver Code
public static void Main()
{
    int N = 3;
    Console.Write("3rd heptacontagon Number is = " +
                               heptacontagonNum(N));
}
}
 
// This code is contributed by Akanksha_Rai

Javascript




<script>
 
// JavaScript program for above approach
 
// Finding the nth heptacontagon number
function heptacontagonNum(n)
{
    return (68 * n * n - 66 * n) / 2;
}
 
// Driver code
 
var N = 3;   
document.write("3rd heptacontagon Number is = " + heptacontagonNum(N));
 
 
</script>
Output: 
3rd heptacontagon Number is = 207

 

Time Complexity: O(1)

Auxiliary Space: O(1)

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

 


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