# Program to check if N is a Centered nonadecagonal number

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

Centered nonadecagonal number represents a dot in the centre and other dots surrounding it in successive nonadecagon(19 sided polygon) layers.The first few Centered nonadecagonal numbers are 1, 20, 58, 115, 191, 286

Examples:

Input: N = 20
Output: Yes
Explanation:
20 is the Second Centered nonadecagonal number is 20.

Input: 38
Output: No
Explanation:
38 is not a Centered nonadecagonal number.

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

Approach: To solve the problem mentioned above we have to know that the Kth term of the Centered nonadecagonal number is given as: As we have to check that the given number can be expressed as a Centered nonadecagonal number or not. This can be checked by generalizing the formula to:

=> => Finally, check the value of computation using this formula if it is an integer, if yes then it means that N is a Centered nonadecagonal number.

Below is the implementation of the above approach:

## C++

 // C++ implementation to check that  // a number is a Centered  // nonadecagonal number or not     #include  using namespace std;     // Function to check that the  // number is a Centered  // nonadecagonal number  bool isCenterednonadecagonal(int N)  {      float n = (19                 + sqrt(152 * N + 209))                / 38;         // Condition to check if the      // number is a Centered      // nonadecagonal number      return (n - (int)n) == 0;  }     // Driver Code  int main()  {      int n = 20;         // Function call      if (isCenterednonadecagonal(n)) {          cout << "Yes";      }      else {          cout << "No";      }      return 0;  }

## Java

 // Java implementation to check that  // a number is a Centered  // nonadecagonal number or not  class GFG{     // Function to check that the  // number is a Centered  // nonadecagonal number  static boolean isCenterednonadecagonal(int N)  {      float n = (float)((19 + Math.sqrt(152 * N +                                         209)) / 38);         // Condition to check if the      // number is a Centered      // nonadecagonal number      return (n - (int)n) == 0;  }     // Driver Code  public static void main(String[] args)  {      int n = 20;         // Function call      if (isCenterednonadecagonal(n))      {          System.out.print("Yes");      }      else      {          System.out.print("No");      }  }  }     // This code is contributed by sapnasingh4991

## Python3

 # Python3 implementation to check that  # a number is a Centered  # nonadecagonal number or not  import math     # Function to check that the  # number is a Centered  # nonadecagonal number  def isCenterednonadecagonal(N):         n = (19 + math.sqrt(152 * N +                          209)) / 38;         # Condition to check if the      # number is a Centered      # nonadecagonal number      return (n - int(n)) == 0;     # Driver Code  n = 20;     # Function call  if (isCenterednonadecagonal(n)):      print("Yes");     else:      print("No");     # This code is contributed by Code_Mech

## C#

 // C# implementation to check that  // a number is a Centered  // nonadecagonal number or not  using System;  class GFG{     // Function to check that the  // number is a Centered  // nonadecagonal number  static bool isCenterednonadecagonal(int N)  {      float n = (float)((19 + Math.Sqrt(152 * N +                                         209)) / 38);         // Condition to check if the      // number is a Centered      // nonadecagonal number      return (n - (int)n) == 0;  }     // Driver Code  public static void Main()  {      int n = 20;         // Function call      if (isCenterednonadecagonal(n))      {          Console.Write("Yes");      }      else     {          Console.Write("No");      }  }  }     // This code is contributed by Nidhi_biet

Output:

Yes


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