# Program to check if N is a Decagonal Number

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

Decagonal Number is a figurate number that extends the concept of triangular and square numbers to the decagon (10-sided polygon). The nth decagonal numbers count the number of dots in a pattern of n nested decagons, all sharing a common corner, where the ith decagon in the pattern has sides made of i dots spaced one unit apart from each other. The first few decagonal numbers are 1, 10, 27, 52, 85, 126, 175, …

Examples:

Input: N = 10
Output: Yes
Explanation:
Second decagonal number is 10.

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 decagonal number is given as 2. As we have to check that the given number can be expressed as a Decagonal 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 Decagonal Number.
4. Else N is not a Decagonal Number.

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach  #include  using namespace std;     // Function to check if N is a  // Decagonal Number  bool isdecagonal(int N)  {      float n          = (3 + sqrt(16 * N + 9))            / 8;         // Condition to check if the      // number is a decagonal number      return (n - (int)n) == 0;  }     // Driver Code  int main()  {      // Given Number      int N = 10;         // Function call      if (isdecagonal(N)) {          cout << "Yes";      }      else {          cout << "No";      }      return 0;  }

## Java

 // Java program for the above approach   import java.lang.Math;     class GFG{         // Function to check if N is a   // decagonal number   public static boolean isdecagonal(int N)   {       double n = (3 + Math.sqrt(16 * N + 9)) / 8;              // Condition to check if the       // number is a decagonal number       return (n - (int)n) == 0;   }      // Driver code      public static void main(String[] args)  {                 // Given number       int N = 10;              // Function call       if (isdecagonal(N))      {           System.out.println("Yes");      }       else      {           System.out.println("No");      }   }  }     // This code is contributed by divyeshrabadiya07

## Python3

 # Python3 program for the above approach  import math     # Function to check if N is a  # decagonal number  def isdecagonal(N):         n = (3 + math.sqrt(16 * N + 9)) / 8            # Condition to check if the      # number is a decagonal number      return (n - int(n)) == 0        # Driver Code  if __name__=='__main__':             # Given number      N = 10            # Function Call      if isdecagonal(N):          print('Yes')      else:          print('No')     # This code is contributed by rutvik_56

## C#

 // C# program for the above approach  using System;     class GFG{         // Function to check if N   // is a decagonal Number  static bool isdecagonal(int N)  {      double n = (3 + Math.Sqrt(16 * N + 9)) / 8;             // Condition to check if the      // number is a decagonal number      return (n - (int)n) == 0;  }         // Driver Code  static public void Main ()  {             // Given Number      int N = 10;             // Function call      if (isdecagonal(N))      {          Console.Write("Yes");      }      else     {          Console.Write("No");      }  }  }     // This code is contributed by ShubhamCoder

Output:

Yes


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