Icosihexagonal Number

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

An Icosihexagon number is class of figurate number. It has 26 – sided polygon called Icosihexagon. The N-th Icosihexagonal number count’s the 26 number of dots and all other dots are surrounding with a common sharing corner and make a pattern. The first few Icosihexagonol numbers are 1, 26, 75, 148 …

Examples:

Input: N = 2
Output: 26
Explanation:
The second Icosihexagonol number is 26.

Input: N = 3
Output: 75



Approach: The N-th Icosihexagonal 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 26 sided polygon is

    Tn =\frac{((26-2)n^2 - (26-4)n)}{2} =\frac{(24n^2 - 22n)}{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 Icosihexagonal Number
int IcosihexagonalNum(int n)
{
    return (24 * n * n - 22 * n) / 2;
}
  
// Driver Code
int main()
{
    int n = 3;
    cout << "3rd Icosihexagonal Number is = "
         << IcosihexagonalNum(n);
  
    return 0;
}
  
// This code is contributed by Code_Mech

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C

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// C program for above approach
#include <stdio.h>
#include <stdlib.h>
  
// Finding the nth Icosihexagonal Number
int IcosihexagonalNum(int n)
{
    return (24 * n * n - 22 * n) / 2;
}
  
// Driver program to test above function
int main()
{
    int n = 3;
    printf("3rd Icosihexagonal Number is = %d",
           IcosihexagonalNum(n));
  
    return 0;
}

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Java

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// Java program for above approach 
class GFG{
      
// Finding the nth icosihexagonal number 
public static int IcosihexagonalNum(int n) 
    return (24 * n * n - 22 * n) / 2
  
// Driver code
public static void main(String[] args)
{
    int n = 3
      
    System.out.println("3rd Icosihexagonal Number is = "
                                    IcosihexagonalNum(n));
}
}
  
// This code is contributed by divyeshrabadiya07

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Python3

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# Python3 program for above approach 
  
# Finding the nth Icosihexagonal Number 
def IcosihexagonalNum(n): 
  
    return (24 * n * n - 22 * n) // 2
  
# Driver Code
n = 3
print("3rd Icosihexagonal Number is = "
                   IcosihexagonalNum(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 icosihexagonal number 
public static int IcosihexagonalNum(int n) 
    return (24 * n * n - 22 * n) / 2; 
  
// Driver code
public static void Main(String[] args)
{
    int n = 3; 
      
    Console.WriteLine("3rd Icosihexagonal Number is = "
                                   IcosihexagonalNum(n));
}
}
  
// This code is contributed by 29AjayKumar

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Output:

3rd Icosihexagonal Number is = 75

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

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