# Hexagonal Number

• Difficulty Level : Basic
• Last Updated : 09 Apr, 2021

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```

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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 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

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## Javascript

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Output:

`10th Hexagonal Number is =  190`

Reference:https://en.wikipedia.org/wiki/Hexagonal_number
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