Octacontagon Number

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

A Octacontagon numberr 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++

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// 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

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C

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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output:

3rd octacontagon Number is = 237

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

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