# Program to check if N is a Centered dodecagonal number

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

Centered Dodecagonal Number represents a dot in the center and other dots surrounding it in successive Dodecagonal Number(12 sided polygon) layers. The first few Centered Dodecagonal Numbers are 1, 13, 37, 73 …

Examples:

Input: N = 13
Output: Yes
Explanation:
Second Centered dodecagonal number is 13.

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 Centered Dodecagonal Number is given as: 2. As we have to check that the given number can be expressed as a Centered Dodecagonal 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 Centered Dodecagonal Number.
4. Else the number N is not a Centered Dodecagonal 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 Centered dodecagonal number  bool isCentereddodecagonal(int N)  {      float n          = (6 + sqrt(24 * N + 12))            / 12;         // Condition to check if N      // is a Centered Dodecagonal Number      return (n - (int)n) == 0;  }     // Driver Code  int main()  {      // Given Number      int N = 13;         // Function call      if (isCentereddodecagonal(N)) {          cout << "Yes";      }      else {          cout << "No";      }      return 0;  }

## Java

 // Java program for the above approach  import java.util.*;     class GFG{     // Function to check if number N  // is a centered dodecagonal number  static boolean isCentereddodecagonal(int N)  {      float n = (float) ((6 + Math.sqrt(24 * N +                                         12)) / 12);         // Condition to check if N is a       // centered dodecagonal number      return (n - (int)n) == 0;  }     // Driver Code  public static void main(String[] args)  {             // Given Number      int N = 13;         // Function call      if (isCentereddodecagonal(N))      {          System.out.print("Yes");      }      else     {          System.out.print("No");      }  }  }     // This code is contributed by sapnasingh4991

## Python3

 # Python3 program for the above approach  import numpy as np     # Function to check if the number N  # is a centered dodecagonal number  def isCentereddodecagonal(N):         n = (6 + np.sqrt(24 * N + 12)) / 12        # Condition to check if N       # is a centered dodecagonal number      return (n - int(n)) == 0    # Driver Code   N = 13    # Function call   if (isCentereddodecagonal(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 number N  // is a centered dodecagonal number  static bool isCentereddodecagonal(int N)  {      float n = (float) ((6 + Math.Sqrt(24 * N +                                         12)) / 12);         // Condition to check if N is a       // centered dodecagonal number      return (n - (int)n) == 0;  }     // Driver Code  public static void Main(string[] args)  {             // Given Number      int N = 13;         // Function call      if (isCentereddodecagonal(N))      {          Console.Write("Yes");      }      else     {          Console.Write("No");      }  }  }     // This code is contributed by rutvik_56

Output:

Yes


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