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Icosihenagonal Number

  • Last Updated : 17 Mar, 2021

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++




// 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;
}

Java




// 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

Python3




# 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

C#




// 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

Javascript




<script>
 
    // Javascript program to find nth
    // Icosihenagonal number
     
    // Function to find
    // Icosihenagonal number
    function Icosihenagonal_num(n)
    {
        // Formula to calculate nth
        // Icosihenagonal number
        return (19 * n * n - 17 * n) / 2;
    }
     
    let n = 3;
    document.write(Icosihenagonal_num(n) + "</br>");
   
    n = 10;
    document.write(Icosihenagonal_num(n));
     
</script>
Output: 
60
865

 

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

 

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