# Hexagonal Number

Given an integer n, the task is to find the nth hexagonal number . The nth hexagonal number Hn is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots when the hexagons are overlaid so that they share one vertex.{Source : wiki}

```Input: n = 2
Output: 6

Input: n = 5
Output: 45

Input: n = 7
Output: 91

```

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

In general, a polygonal number (triangular number, square number, etc) is a number represented as dots or pebbles arranged in the shape of a regular polygon. The first few pentagonal numbers are 1, 5, 12, etc.
If s is the number of sides in a polygon, the formula for the nth s-gonal number P (s, n) is

```nth s-gonal number P(s, n) = (s - 2)n(n-1)/2 + n

If we put s = 6, we get

n'th Hexagonal number Hn = 2(n*n)-n
= n(2n - 1)
```

## C/C++

 `// C program for above approach ` `#include ` `#include ` ` `  `// Finding the nth Hexagonal Number ` `int` `hexagonalNum(``int` `n) ` `{ ` `    ``return` `n*(2*n - 1); ` `} ` ` `  `// Driver program to test above function ` `int` `main() ` `{ ` `    ``int` `n = 10; ` `    ``printf``(``"10th Hexagonal Number is = %d"``, ` `                             ``hexagonalNum(n)); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program for above approach ` `class` `Hexagonal ` `{ ` `    ``int` `hexagonalNum(``int` `n) ` `    ``{ ` `        ``return` `n*(``2``*n - ``1``); ` `    ``} ` `} ` ` `  `public` `class` `GeeksCode ` `{ ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``Hexagonal obj = ``new` `Hexagonal(); ` `        ``int` `n = ``10``; ` `        ``System.out.printf(``"10th Hexagonal number is = "` `                          ``+ obj.hexagonalNum(n)); ` `    ``} ` `} `

## Python

 `# Python program for finding Hexagonal numbers ` `def` `hexagonalNum( n ): ` `    ``return` `n``*``(``2``*``n ``-` `1``) ` ` `  `# Driver code ` `n ``=` `10` `print` `"10th Hexagonal Number is = "``, hexagonalNum(n) `

## C#

 `// C# program for above approach ` `using` `System; ` ` `  `class` `GFG { ` `     `  `    ``static` `int` `hexagonalNum(``int` `n) ` `    ``{ ` `        ``return` `n * (2 * n - 1); ` `    ``} ` ` `  `    ``public` `static` `void` `Main() ` `    ``{ ` `     `  `        ``int` `n = 10; ` `         `  `        ``Console.WriteLine(``"10th Hexagonal"` `        ``+ ``" number is = "` `+ hexagonalNum(n)); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## PHP

 ` `

Output:

```10th Hexagonal Number is =  190
```

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