# Program to check if N is a Centered Octadecagonal number

Given an integer N, the task is to check if it is a Centered Octadecagonal number or not. Print “yes” if it is otherwise output is “no”.

Centered Octadecagonal number represents a dot in the centre and others dot are arranged around it in successive layers of octadecagon(18 sided polygon). The first few Centered Octadecagonal numbers are 1, 19, 55, 109, 181, 271, 379, …

Examples:

Input: N = 19
Output: Yes
Explanation:
19 is the Second Centered Octadecagonal number is 19.

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

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

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

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

Below is the implementation of the above approach:

## C++

 // C++ implementation to check that  // a number is a Centered  // Octadecagonal number or not     #include  using namespace std;     // Function to check that the  // number is a Centered  // Octadecagonal number  bool isCenteredOctadecagonal(int N)  {         // Implement the formula generated      float n = (9 + sqrt(36 * N + 45)) / 18;         // Condition to check if the      // number is a Centered      // Octadecagonal number      return (n - (int)n) == 0;  }     // Driver Code  int main()  {      int n = 19;         // Function call      if (isCenteredOctadecagonal(n)) {          cout << "Yes";      }      else {          cout << "No";      }      return 0;  }

## Java

 // Java implementation to check that   // a number is a centered   // octadecagonal number or not   import java.lang.Math;     class GFG{         // Function to check that the   // number is a centered   // octadecagonal number   public static boolean isCenteredOctadecagonal(int N)   {              // Implement the formula generated       double n = (9 + Math.sqrt(36 * N + 45)) / 18;              // Condition to check if the       // number is a Centered       // Octadecagonal number       return(n - (int)n) == 0;   }      // Driver Code      public static void main(String[] args)  {      int n = 19;          // Function call       if (isCenteredOctadecagonal(n))      {           System.out.println("Yes");      }       else     {           System.out.println("No");      }   }  }     // This code is contributed by divyeshrabadiya07

## Python3

 # Python3 implementation to check that   # a number is a centered octadecagonal  # number or not   import math     # Function to check that the   # number is a centered   # octadecagonal number   def isCenteredOctadecagonal(N):             # Implement the formula generated      n = (9 + math.sqrt(36 * N + 45)) / 18;              # Condition to check if the       # number is a centered       # octadecagonal number       return (n - int(n)) == 0    # Driver code   if __name__=='__main__':             n = 19            # Function call      if isCenteredOctadecagonal(n):          print('Yes')      else:          print('No')     # This code is contributed by rutvik_56

## C#

 // C# implementation to check that  // a number is a centered  // octadecagonal number or not  using System;     class GFG{     // Function to check that the  // number is a centered  // octadecagonal number  static bool isCenteredOctadecagonal(int N)  {         // Implement the formula generated      double n = (9 + Math.Sqrt(36 * N + 45)) / 18;             // Condition to check if the      // number is a Centered      // octadecagonal number      return (n - (int)n) == 0;  }         // Driver Code  static public void Main ()  {      int n = 19;             // Function call      if (isCenteredOctadecagonal(n))      {          Console.Write("Yes");      }      else     {          Console.Write("No");      }  }  }     //This code is contributed by ShubhamCoder

Output:

Yes


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