A Carol number is an integer of the form 4^{n} – 2^{(n+1)} – 1. An equivalent formula is (2^{n}-1)^{2} – 2.

**An Interesting Property :**

For n > 2, the binary representation of the n-th Carol number is n-2 consecutive one’s, a single zero in the middle, and n + 1 more consecutive one’s. Example, n = 4 carol number is 223 and binary of 223 is 11011111, here n-2 = 4-2 = 2 consecutive one’s in starting then single 0 in middle and then n + 1 = 4 + 1 = 5 consecutive one’s after it.

Given a number n, the task is to find the n’th Carol Number. First few carol numbers are 1, 7, 47, 223, 959… etc.

**Examples :**

Input : n = 2 Output: 7 Input : n = 4 Output: 223

## C++

`// C++ program to find n'th Carol number` `#include <bits/stdc++.h>` `using` `namespace` `std;` ` ` `// Function to find n'th carol number` `int` `carol(` `int` `n)` `{` ` ` `int` `result = ` `pow` `(2, n) - 1;` ` ` `return` `result * result - 2;` `}` ` ` `// Driver program to ru the case` `int` `main()` `{` ` ` `int` `n = 4;` ` ` `cout << carol(n);` ` ` `return` `0;` `}` |

## Python

`# Python program to find n'th Carol number` `def` `carol(n):` ` ` `# a**b is a ^ b in python` ` ` `result ` `=` `(` `2` `*` `*` `n) ` `-` `1` ` ` `return` `result ` `*` `result ` `-` `2` ` ` `# driver program to run the case` `n ` `=` `4` `print` `carol(n)` |

## Java

`/* Java program to find n'th Carol number */` `class` `GFG {` ` ` `static` `int` `carol(` `int` `n)` ` ` `{` ` ` `double` `tmp = Math.pow(` `2` `, n) - ` `1` `;` ` ` `return` `(` `int` `)tmp;` ` ` `}` ` ` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `n = ` `4` `;` ` ` `System.out.println(carol(n));` ` ` `}` `}` |

## C#

`/* C# program to find n'th Carol number */` `using` `System;` ` ` `class` `GFG {` ` ` `static` `int` `carol(` `int` `n)` ` ` `{` ` ` `int` `result = (` `int` `)Math.Pow(2, n) - 1;` ` ` `return` `result * result - 2;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `n = 4;` ` ` `Console.WriteLine(carol(n));` ` ` `}` `}` ` ` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP program to find` `// n'th Carol number` ` ` `// Function to find` `// n'th carol number` `function` `carol(` `$n` `)` `{` ` ` `$result` `= pow(2, ` `$n` `) - 1;` ` ` `return` `$result` `* ` `$result` `- 2;` `}` ` ` `// Driver Code` `$n` `= 4;` `echo` `carol(` `$n` `);` ` ` `// This code is contributed by ajit` `?>` |

**Output :**

223

Reference:

https://en.wikipedia.org/wiki/Carol_number

This article is contributed by **Shashank Mishra ( Gullu )**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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