# Program to check if N is a Centered Triangular Number

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

Centered triangular number is a centered polygonal number that represents a triangle with a dot in the centre and all other dots surrounding the centre in successive triangular layers . The first few Centered triangular numbers are 1, 4, 10, 19, 31, 46, 64, 85, 109, 136, …

Examples:

Input: N = 4
Output: Yes

Input: 20
Output: No

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

Approach:

• The Kth Centered triangular number can be expressed as: • In order to check if the given number N can be expressed as a Centered triangular number or not, we need to check if gives an integer or not.

Below is the implementation of the above approach:

## C++

 // C++ implementation to check  // whether a given number is a  // Centered triangular number or not  #include  using namespace std;     // Function to check if the  // number is a Centered  // Triangular Number  bool isCenteredtriangular(int N)  {      float K = (-3                 + sqrt(24 * N - 15))                / 6;         // Condition for K to be      // an integer      return (K - (int)K) == 0;  }     // Driver Code  int main()  {      int N = 85;      if (isCenteredtriangular(N)) {          cout << "Yes";      }      else {          cout << "No";      }      return 0;  }

## Java

 // Java implementation to check that   // a number is a centered triangular  // number or not   import java.lang.Math;     class GFG{         // Function to check that the number  // is a centered triangular number   public static boolean isCenteredTriangular(int N)   {       double K = (-3 + Math.sqrt(24 * N - 15)) / 6;         // Condition to check if the number      // is a centered triangular number       return (K - (int)K) == 0;   }      // Driver Code  public static void main(String[] args)   {      int N = 85;          // Function call       if (isCenteredTriangular(N))       {           System.out.println("Yes");      }       else     {           System.out.println("No");      }   }  }     // This code is contributed by ShubhamCoder

## Python3

 # Python3 implementation to check  # whether a given number is a  # Centered triangular number or not  import math     # Function to check if the  # number is a Centered  # Triangular Number  def isCenteredtriangular(N):             K = (-3 + math.sqrt(24 * N - 15)) / 6            # Condition for K to be      # an integer      if (K - int(K)) == 0:          return True                return False    # Driver Code     # Given Number  N = 85    # Function call  if (isCenteredtriangular(N)):      print("Yes")  else:      print("No")     # This code is contributed by shubhamsingh10

## C#

 // C# implementation to check whether   // a given number is a centered   // triangular number or not  using System;     class GFG{     // Function to check if the number   // is a centered triangular number  static bool isCenteredtriangular(int N)  {      double K = (-3 + Math.Sqrt(24 * N - 15)) / 6;             // Condition for K to be      // an integer      return (K - (int)K) == 0;  }         // Driver Code  static public void Main ()  {      int N = 85;      if (isCenteredtriangular(N))      {          Console.Write("Yes");      }      else     {          Console.Write("No");      }  }  }     // This code is contributed by shubhamsingh10

Output:

Yes


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Improved By : SHUBHAMSINGH10

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