# Program to check if N is a Enneadecagonal Number

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

Enneadecagonal Number is a 19-sided polygon in mathematics. It belongs to a class of figurative number. The number contains the number of dots and the dots are arranged in a pattern or series. An Enneadecagonal Number is also known as Nonadecagon. The dots have common points and all other dots are arrange in the successive layer. The nth Enneadecagonal Number counts the seventeen number of dots and all the other dots are surrounding with a common sharing corner and make a pattern. The first few Enneadecagonal Numbers are 1, 19, 54, 106, 175…

Examples:

Input: N = 19
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 Enneadecagonal Number is given as 2. As we have to check that the given number can be expressed as a Enneadecagonal 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 Enneadecagonal Number.
4. Else N is not a Enneadecagonal Number.

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach  #include  using namespace std;     // Function to check if number N  // is a enneadecagonal number  bool isenneadecagonal(int N)  {      float n          = (15 + sqrt(136 * N + 225))            / 34;         // Condition to check if N is a      // enneadecagonal number      return (n - (int)n) == 0;  }     // Driver Code  int main()  {      // Given Number      int N = 19;         // Function call      if (isenneadecagonal(N)) {          cout << "Yes";      }      else {          cout << "No";      }      return 0;  }

## Java

 // Java program for the above approach  class GFG{     // Function to check if number N  // is a enneadecagonal number  static boolean isenneadecagonal(int N)  {      float n = (float)(15 + Math.sqrt(136 * N +                                       225)) / 34;         // Condition to check if N is a      // enneadecagonal number      return (n - (int)n) == 0;  }     // Driver Code  public static void main(String[] args)  {             // Given Number      int N = 19;         // Function call      if (isenneadecagonal(N))      {          System.out.println("Yes");      }      else     {          System.out.println("No");      }  }  }     // This code is contributed by rutvik_56

## Python3

 # Python3 program for the above approach   import math     # Function to check if number N   # is a enneadecagonal number   def isenneadecagonal(N):         n = (15 + math.sqrt(136 * N + 225)) / 34        # Condition to check if N is a       # enneadecagonal number       return (n - int(n)) == 0    # Driver Code   N = 19    # Function call   if (isenneadecagonal(N)):      print("Yes")   else:       print("No")      # This code is contributed by divyamohan123

## C#

 // C# program for the above approach  using System;     class GFG{     // Function to check if number N  // is a enneadecagonal number  static bool isenneadecagonal(int N)  {      float n = (float)(15 + Math.Sqrt(136 * N +                                       225)) / 34;             // Condition to check if N is a      // enneadecagonal number      return (n - (int)n) == 0;  }         // Driver Code  static public void Main ()  {                 // Given number      int N = 19;             // Function call      if (isenneadecagonal(N))      {          Console.Write("Yes");      }      else     {          Console.Write("No");      }  }  }     // This code is contributed by shubhamsingh10

Output:

Yes


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