Enneacontagon Number

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

A Enneacontagon number. is class of figurate number. It has 90 – sided polygon called enneacontagon. The N-th enneacontagon number count’s the 90 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few enneacontagonol numbers are 1, 90, 267, 532 …

Examples:

Input: N = 2
Output: 90
Explanation:
The second enneacontagonol number is 90.

Input: N = 3
Output: 267



Approach: The N-th enneacontagon 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 90 sided polygon is

    Tn =\frac{((90-2)n^2 - (90-4)n)}{2} =\frac{(88n^2 - 86)}{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 enneacontagon Number
int enneacontagonNum(int n)
{
    return (88 * n * n - 86 * n) / 2;
}
  
// Driver Code
int main()
{
    int n = 3;
    cout << "3rd enneacontagon Number is = "
         << enneacontagonNum(n);
  
    return 0;
}
  
// This code is contributed by Akanksha_Rai

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C

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// C program for above approach
#include <stdio.h>
#include <stdlib.h>
  
// Finding the nth enneacontagon Number
int enneacontagonNum(int n)
{
    return (88 * n * n - 86 * n) / 2;
}
  
// Driver program to test above function
int main()
{
    int n = 3;
    printf("3rd enneacontagon Number is = %d",
           enneacontagonNum(n));
  
    return 0;
}

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Java

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// Java program for above approach
class GFG{
  
// Finding the nth enneacontagon number 
public static int enneacontagonNum(int n) 
    return (88 * n * n - 86 * n) / 2
  
// Driver code    
public static void main(String[] args)
{
    int n = 3
  
    System.out.println("3rd enneacontagon Number is = "
                                    enneacontagonNum(n));
}
}
  
// This code is contributed by divyeshrabadiya07 

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Python3

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# Python3 program for above approach 
  
# Finding the nth enneacontagon Number 
def enneacontagonNum(n): 
  
    return (88 * n * n - 86 * n) // 2
  
# Driver Code
n = 3
print("3rd enneacontagon Number is = ",
                   enneacontagonNum(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 enneacontagon number 
public static int enneacontagonNum(int n) 
    return (88 * n * n - 86 * n) / 2; 
  
// Driver code 
public static void Main(String[] args)
{
    int n = 3; 
  
    Console.WriteLine("3rd enneacontagon Number is = "
                                   enneacontagonNum(n));
}
}
  
// This code is contributed by Rajput-Ji

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Output:

3rd enneacontagon Number is = 267

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

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