Icosihenagonal Number

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

An Icosihenagonal number is class of figurate number. It has 21 – sided polygon called Icosihenagon. The n-th Icosihenagonal number counts the 21 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few Icosihenagonal numbers are 1, 21, 60, 118, 195, 291, 406 …

Examples:

Input: N = 2
Output: 21
Explanation:
The second Icosihenagonal number is 21

Input: N = 6
Output: 291



Approach: In mathematics, the Nth Icosihenagonal number is given by the formula:

Tn = (19n^2 - 17n)/2

Below is the implementation of the above approach:

C++

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// C++ program to find nth
// Icosihenagonal number
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to find
// Icosihenagonal number
int Icosihenagonal_num(int n)
{
    // Formula to calculate nth
    // Icosihenagonal number
    return (19 * n * n - 17 * n) / 2;
}
  
// Driver Code
int main()
{
    int n = 3;
    cout << Icosihenagonal_num(n) << endl;
  
    n = 10;
    cout << Icosihenagonal_num(n) << endl;
  
    return 0;
}

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Java

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// Java program to find nth
// Icosihenagonal number
class GFG{
  
// Function to find
// Icosihenagonal number
static int Icosihenagonal_num(int n)
{
    // Formula to calculate nth
    // Icosihenagonal number
    return (19 * n * n - 17 * n) / 2;
}
  
// Driver Code
public static void main(String[] args)
{
    int n = 3;
    System.out.print(Icosihenagonal_num(n) + "\n");
  
    n = 10;
    System.out.print(Icosihenagonal_num(n) + "\n");
}
}
  
// This code is contributed by Rajput-Ji

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Python3

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# Python3 program to find nth 
# icosihenagonal number 
  
# Function to find 
# icosihenagonal number 
def Icosihenagonal_num(n):
      
    # Formula to calculate nth 
    # icosihenagonal number
    return (19 * n * n - 17 * n) / 2
      
# Driver Code
n = 3
print(int(Icosihenagonal_num(n)))
  
n = 10
print(int(Icosihenagonal_num(n)))
  
# This code is contributed by divyeshrabadiya07

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C#

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// C# program to find nth
// Icosihenagonal number
using System;
  
class GFG{
  
// Function to find
// Icosihenagonal number
static int Icosihenagonal_num(int n)
{
    // Formula to calculate nth
    // Icosihenagonal number
    return (19 * n * n - 17 * n) / 2;
}
  
// Driver Code
public static void Main()
{
    int n = 3;
    Console.Write(Icosihenagonal_num(n) + "\n");
  
    n = 10;
    Console.Write(Icosihenagonal_num(n) + "\n");
}
}
  
// This code is contributed by Code_Mech

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Output:

60
865

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

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