# Program to check if N is an Icosikaioctagonal Number

Given an integer N, the task is to check if it is a icosikaioctagonal number or not.

An icosikaioctagonal number is class of figurate number. It has 28 – sided polygon called icosikaioctagon. The N-th icosikaioctagonal number count’s the 28 number of dots and all other dots are surrounding with a common sharing corner and make a pattern. The first few icosikaioctagonol numbers are 1, 28, 81, 160 …

Examples:

Input: N = 28
Output: Yes
Explanation:
Second icosikaioctagonal number is 28.

Input: 30
Output: No

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

1. The Kth term of the icosikaioctagonal number is given as: 2. As we have to check that the given number can be expressed as a icosikaioctagonal number or not. This can be checked as follows –

=> => 3. Finally, check the value of computed using this formulae is an integer, which means that N is a icosikaioctagonal number.

Below is the implementation of the above approach:

## C++

 // C++ program to check whether a  // number is an icosikaioctagonal   // number or not     #include     using namespace std;     // Function to check whether a number  // is an icosikaioctagonal number or not  bool isicosikaioctagonal(int N)  {      float n          = (24 + sqrt(208 * N + 576))            / 52;         // Condition to check if the      // number is an       // icosikaioctagonal number      return (n - (int)n) == 0;  }     // Driver code  int main()  {      int i = 28;         if (isicosikaioctagonal(i)) {          cout << "Yes";      }      else {          cout << "No";      }      return 0;  }

## Java

 // Java program to check whether a  // number is an icosikaioctagonal   // number or not  class GFG{      // Function to check whether a  // number is an icosikaioctagonal   // number or not  static boolean isicosikaioctagonal(int N)   {       float n = (float) ((24 + Math.sqrt(208 * N +                                          576)) / 52);             // Condition to check whether a      // number is an icosikaioctagonal       // number or not      return (n - (int)n) == 0;   }      // Driver Code   public static void main(String[] args)   {              // Given number       int N = 28;              // Function call       if (isicosikaioctagonal(N))       {           System.out.print("Yes");       }       else     {           System.out.print("No");       }   }   }      // This code is contributed by shubham

## Python3

 # Python3 program to check whether a  # number is an icosikaioctagonal   # number or not  import math     # Function to check whether a number  # is an icosikaioctagonal number or not  def isicosikaioctagonal(N):         n = (24 + math.sqrt(208 * N +                         576)) // 52;         # Condition to check if the      # number is an       # icosikaioctagonal number      return (n - int(n)) == 0;     # Driver code  i = 28;     if (isicosikaioctagonal(i)):      print("Yes");  else:      print("No");     # This code is contributed by Code_Mech

## C#

 // C# program to check whether a  // number is an icosikaioctagonal   // number or not  using System;  class GFG{      // Function to check whether a  // number is an icosikaioctagonal   // number or not  static bool isicosikaioctagonal(int N)   {       float n = (float)((24 + Math.Sqrt(208 * N +                                         576)) / 52);             // Condition to check whether a      // number is an icosikaioctagonal       // number or not      return (n - (int)n) == 0;   }      // Driver Code   public static void Main()   {              // Given number       int N = 28;              // Function call       if (isicosikaioctagonal(N))       {           Console.Write("Yes");       }       else     {           Console.Write("No");       }   }   }      // This code is contributed by Code_Mech

Output:

Yes


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