# Program to check if N is a Icosidigonal Number

Given an integer N, the task is to check if it is a Icosidigonal Number or not. If the number N is an Icosidigonal Number then print “Yes” else print “No”.

Icosidigonal number:
The polygon has many gons, depends on their gonal number series. In mathematics, there are a number of gonal numbers and the Icosidigonal Number is one of them and these numbers have 22 -sided polygon(icosidigon). An Icosidigonal Number belong to the class of figurative number. They have one common dots points and other dots pattern is arranged in an n-th nested Icosidigon pattern.
The first few Icosidigonal numbers are 1, 22, 63, 124, 205, 306…

Examples:

Input: N = 22
Output: Yes
Explanation:
Second Icosidigonal number is 22.

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 Icosidigonal number is given as 2. As we have to check that the given number can be expressed as a Icosidigonal Number or not. This can be checked as follows –

=> => 3. If the value of K calculated using the above formula is an integer, then N is a Icosidigonal Number.
4. Else N is not a Icosidigonal Number.

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach  #include  using namespace std;     // Function to check if the number N  // is a Icosidigonal number  bool isIcosidigonal(int N)  {      float n          = (18 + sqrt(160 * N + 324))            / 40;         // Condition to check if the      // number is a Icosidigonal number      return (n - (int)n) == 0;  }     // Driver Code  int main()  {      // Given Number      int N = 22;         // Function call      if (isIcosidigonal(N)) {          cout << "Yes";      }      else {          cout << "No";      }      return 0;  }

## Java

 // Java program for the above approach  class GFG{     // Function to check if the number N  // is a icosidigonal number  static boolean isIcosidigonal(int N)  {      float n = (float) ((18 + Math.sqrt(160 * N +                                          324)) / 40);         // Condition to check if the number       // is a icosidigonal number      return (n - (int)n) == 0;  }     // Driver Code  public static void main(String[] args)  {             // Given number      int N = 22;         // Function call      if (isIcosidigonal(N))      {          System.out.print("Yes");      }      else      {          System.out.print("No");      }  }  }     // This code is contributed by Amit Katiyar

## Python3

 # Python3 program for the above approach  import numpy as np     # Function to check if the number N  # is a icosidigonal number  def isIcosidigonal(N):         n = (18 + np.sqrt(160 * N + 324)) / 40        # Condition to check if N       # is a icosidigonal number      return (n - int(n)) == 0    # Driver Code   N = 22    # Function call   if (isIcosidigonal(N)):      print ("Yes")   else:      print ("No")     # This code is contributed by PratikBasu

## C#

 // C# program for the above approach   using System;     class GFG{      // Function to check if the number N   // is a icosidigonal number   static bool isIcosidigonal(int N)   {       float n = (float) ((18 + Math.Sqrt(160 * N +                                       324)) / 40);          // Condition to check if the number       // is a icosidigonal number       return (n - (int)n) == 0;   }      // Driver Code   public static void Main(string[] args)   {              // Given number       int N = 22;          // Function call       if (isIcosidigonal(N))       {           Console.Write("Yes");       }       else     {           Console.Write("No");       }   }   }      // This code is contributed by rutvik_56

Output:

Yes


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