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Octacontagon Number

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

A Octacontagon number is class of figurate number. It has 80 – sided polygon called octacontagon. The N-th octacontagon number count’s the 80 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few octacontagonol numbers are 1, 80, 237, 472 … 
 

Examples: 

Input: N = 2 
Output: 80 
Explanation: 
The second octacontagonol number is 80. 

Input: N = 3 
Output: 237 

Approach: The N-th octacontagon 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 80 sided polygon is

Tn =\frac{((80-2)n^2 - (80-4)n)}{2} =\frac{(78n^2 - 76n)}{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 octacontagon Number
int octacontagonNum(int n)
{
    return (78 * n * n - 76 * n) / 2;
}
 
// Driver Code
int main()
{
    int n = 3;
    cout <<"3rd octacontagon Number is = "
         << octacontagonNum(n);
 
    return 0;
}
 
// This code is contributed by shivanisinghss2110

                    

C

// C program for above approach
#include <stdio.h>
#include <stdlib.h>
 
// Finding the nth octacontagon Number
int octacontagonNum(int n)
{
    return (78 * n * n - 76 * n) / 2;
}
 
// Driver program to test above function
int main()
{
    int n = 3;
    printf("3rd octacontagon Number is = %d",
           octacontagonNum(n));
 
    return 0;
}

                    

Java

// Java program for above approach
import java.util.*;
class GFG{
 
// Finding the nth octacontagon Number
static int octacontagonNum(int n)
{
    return (78 * n * n - 76 * n) / 2;
}
 
// Driver Code
public static void main(String args[])
{
    int n = 3;
    System.out.print("3rd octacontagon Number is = " +
                                  octacontagonNum(n));
}
}
 
// This code is contributed by Akanksha_Rai

                    

Python3

# Python3 program for above approach
 
# Finding the nth octacontagon number
def octacontagonNum(n):
 
    return (78 * n * n - 76 * n) // 2
 
# Driver code
n = 3
print("3rd octacontagon Number is = ",
                   octacontagonNum(n))
 
# This code is contributed by divyamohan123

                    

C#

// C# program for above approach
using System;
class GFG{
 
// Finding the nth octacontagon Number
static int octacontagonNum(int n)
{
    return (78 * n * n - 76 * n) / 2;
}
 
// Driver Code
public static void Main()
{
    int n = 3;
    Console.Write("3rd octacontagon Number is = " +
                               octacontagonNum(n));
}
}
 
// This code is contributed by Akanksha_Rai

                    

Javascript

<script>
 
// Javascript program for above approach
 
// Finding the nth octacontagon Number
function octacontagonNum(n)
{
    return (78 * n * n - 76 * n) / 2;
}
 
// Driver Code
var n = 3;
document.write("3rd octacontagon Number is = " + octacontagonNum(n));
 
 
</script>

                    

Output: 
3rd octacontagon Number is = 237

 

Time Complexity: O(1)

Auxiliary Space: O(1)

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



Last Updated : 07 Oct, 2021
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