Octadecagonal Number

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

An Octadecagonal number is a class of figurate numbers. It has 18 – sided polygon called Octadecagon. The Nth Octadecagonal number count’s the eighteen number of dots and all other dots are surrounding with a common sharing corner and make a pattern. The first few Octadecagonal numbers are 1, 18, 51, 100, 165, 246, 343 …

Examples:

Input: N = 2
Output: 18
Explanation:
The second octadecagonal number is 18.

Input: N = 6
Output: 246



Approach: The Nth Octadecagonal number is given by the formula:

Tn = (16n^2 - 14n)/2

Below is the implementation of the above approach:

C++

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// C++ program to find Nth
// Octadecagonal number
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to find N-th
// Octadecagonal number
int Octadecagonal_num(int n)
{
    // Formula to calculate nth
    // Octadecagonal number
    return (16 * n * n - 14 * n) / 2;
}
  
// Driver code
int main()
{
    int n = 3;
    cout << Octadecagonal_num(n) << endl;
  
    n = 10;
    cout << Octadecagonal_num(n) << endl;
  
    return 0;
}

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Java

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// Java program to find Nth
// octadecagonal number
import java.io.*; 
import java.util.*; 
  
class GFG{ 
      
// Function to find N-th
// octadecagonal number
static int Octadecagonal_num(int n)
{
          
    // Formula to calculate nth
    // octadecagonal number
    return (16 * n * n - 14 * n) / 2;
}
      
// Driver code 
public static void main(String[] args) 
    int n = 3;
    System.out.println(Octadecagonal_num(n));
      
    n = 10;
    System.out.println(Octadecagonal_num(n));
  
// This code is contributed by coder001

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Python3

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# Python3 program to find Nth 
# octadecagonal number
  
# Function to find N-th 
# octadecagonal number
def Octadecagonal_num(n):
      
    # Formula to calculate nth 
    # octadecagonal number 
    return (16 * n * n - 14 * n) / 2
  
# Driver code    
n = 3
print(int(Octadecagonal_num(n))) 
  
n = 10
print(int(Octadecagonal_num(n))) 
  
# This code is contributed by divyeshrabadiya07     

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C#

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// C# program to find Nth
// octadecagonal number
using System; 
  
class GFG{ 
      
// Function to find N-th
// octadecagonal number
static int Octadecagonal_num(int n)
{
          
    // Formula to calculate nth
    // octadecagonal number
    return (16 * n * n - 14 * n) / 2;
}
      
// Driver code 
public static void Main(string[] args) 
    int n = 3;
    Console.Write(Octadecagonal_num(n) + "\n");
      
    n = 10;
    Console.Write(Octadecagonal_num(n) + "\n");
  
// This code is contributed by rutvik_56

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Output:

51
730

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

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