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

Centered Decagonal Numberis centered figurative number that represents a decagon with dot in center and all other dot surrounding it in successive Decagonal Number form. The first few Centered decagonal numbers are1, 11, 31, 61, 101, 151 …

**Examples:**

Input:N = 11Output:YesExplanation:

Second Centered decagonal number is 11.

Input:N = 30Output:No

**Approach:**

1. The** K ^{th}** term of the Centered Decagonal Number is given as

2. As we have to check that the given number can be expressed as a Centered Decagonal Number or not. This can be checked as follows:

=>

=>

3. If the value of **K** calculated using the above formula is an integer, then **N** is a Centered Decagonal Number.

4. Else the number **N** is not a Centered Decagonal Number.

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to check if number N` `// is a Centered decagonal number` `bool` `isCentereddecagonal(` `int` `N)` `{` ` ` `float` `n` ` ` `= (5 + ` `sqrt` `(20 * N + 5))` ` ` `/ 10;` ` ` `// Condition to check if N` ` ` `// is Centered Decagonal Number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `N = 11;` ` ` `// Function call` ` ` `if` `(isCentereddecagonal(N)) {` ` ` `cout << ` `"Yes"` `;` ` ` `}` ` ` `else` `{` ` ` `cout << ` `"No"` `;` ` ` `}` ` ` `return` `0;` `}` |

## Java

`// Java implementation to check that a number` `// is a centered decagonal number or not` `import` `java.lang.Math;` `class` `GFG{` ` ` `// Function to check that the number` `// is a centered decagonal number` `public` `static` `boolean` `isCentereddecagonal(` `int` `N)` `{` ` ` `double` `n = (` `5` `+ Math.sqrt(` `20` `* N + ` `5` `)) / ` `10` `;` ` ` `// Condition to check if the number` ` ` `// is a centered decagonal number` ` ` `return` `(n - (` `int` `)n) == ` `0` `;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `n = ` `11` `;` ` ` `// Function call` ` ` `if` `(isCentereddecagonal(n))` ` ` `{` ` ` `System.out.println(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `System.out.println(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by ShubhamCoder` |

## Python3

`# Python3 program for the above approach` `import` `numpy as np` `# Function to check if the number N` `# is a centered decagonal number` `def` `isCentereddecagonal(N):` ` ` `n ` `=` `(` `5` `+` `np.sqrt(` `20` `*` `N ` `+` `5` `)) ` `/` `10` ` ` `# Condition to check if N` ` ` `# is centered decagonal number` ` ` `return` `(n ` `-` `int` `(n)) ` `=` `=` `0` `# Driver Code` `N ` `=` `11` `# Function call` `if` `(isCentereddecagonal(N)):` ` ` `print` `(` `"Yes"` `)` `else` `:` ` ` `print` `(` `"No"` `)` `# This code is contributed by PratikBasu` |

## C#

`// C# implementation to check that a number` `// is a centered decagonal number or not` `using` `System;` `class` `GFG{` ` ` `// Function to check that the number` `// is a centered decagonal number` `static` `bool` `isCentereddecagonal(` `int` `N)` `{` ` ` `double` `n = (5 + Math.Sqrt(20 * N + 5)) / 10;` ` ` ` ` `// Condition to check if the number` ` ` `// is a centered decagonal number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` ` ` `// Driver Code` `static` `public` `void` `Main ()` `{` ` ` `int` `n = 11;` ` ` ` ` `// Function call` ` ` `if` `(isCentereddecagonal(n))` ` ` `{` ` ` `Console.Write(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `Console.Write(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by ShubhamCoder` |

## Javascript

`<script>` `// Javascript program for the above approach` `// Function to check if number N` `// is a Centered decagonal number` `function` `isCentereddecagonal(N)` `{` ` ` `let n` ` ` `= (5 + Math.sqrt(20 * N + 5))` ` ` `/ 10;` ` ` `// Condition to check if N` ` ` `// is Centered Decagonal Number` ` ` `return` `(n - parseInt(n)) == 0;` `}` `// Driver Code` `let N = 11;` `// Function call` `if` `(isCentereddecagonal(N)) {` `document.write(` `"Yes"` `);` `}` `else` `{` `document.write(` `"No"` `);` `}` `</script>` |

**Output:**

Yes

**Time Complexity: **O(1)

**Auxiliary Space: **O(1)

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