# Program to check if N is a Octadecagon number

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

Octadecagon Number is a 18-sided polygon. The first few Octadecagon Numbers are 1, 18, 51, 100, 165, 246, 343, …

Examples:

Input: N = 18
Output: Yes
Explanation:

Input: N = 30
Output: No

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

Approach:

1. The Kth term of the Octadecagon number is given as

2. As we have to check that the given number can be expressed as a Octadecagon Number or not. This can be checked as:

=>
=>

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

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach  #include  using namespace std;     // Function to check if N is a  // Octadecagon Number  bool isOctadecagon(int N)  {      float n          = (14 + sqrt(128 * N + 196))            / 32;         // Condition to check if the      // number is a Octadecagon number      return (n - (int)n) == 0;  }     // Driver Code  int main()  {      // Given Number      int N = 18;         // Function call      if (isOctadecagon(N)) {          cout << "Yes";      }      else {          cout << "No";      }      return 0;  }

## Java

 // Java program for the above approach   import java.lang.Math;     class GFG{         // Function to check if N is a   // octadecagon Number   public static boolean isOctadecagon(int N)   {       double n = (14 + Math.sqrt(128 * N +                                  196)) / 32;              // Condition to check if the       // number is a octadecagon number       return (n - (int)n) == 0;   }      // Driver Code      public static void main(String[] args)   {                 // Given Number       int N = 18;              // Function call       if (isOctadecagon(N))      {           System.out.println("Yes");      }       else      {           System.out.println("No");      }   }  }     // This code is contributed by divyeshrabadiya07

## Python3

 # Python3 program for the above approach  import math     # Function to check if N is a  # octadecagon number  def isOctadecagon(N):         n = (14 + math.sqrt(128 * N + 196)) // 32            # Condition to check if the      # number is a octadecagon number      return ((n - int(n)) == 0)     # Driver code   if __name__=='__main__':             # Given number      N = 18            # Function Call      if isOctadecagon(N):          print('Yes')      else:          print('No')     # This code is contributed by rutvik_56

Output:

Yes


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