# 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

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 H_{n}= 2(n*n)-n = n(2n - 1)

## C

`// C program for above approach` `#include <stdio.h>` `#include <stdlib.h>` `// 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

`<?php` `// PHP program for above approach` `// Finding the nth Hexagonal Number` `function` `hexagonalNum(` `$n` `)` `{` ` ` `return` `$n` `* (2 * ` `$n` `- 1);` `}` `// Driver program to test above function` `$n` `= 10;` `echo` `(` `"10th Hexagonal Number is "` `.` ` ` `hexagonalNum(` `$n` `));` `// This code is contributed by Ajit.` `?>` |

## Javascript

`<script>` `// Javascript program for above approach` `// centered pentadecagonal function` `function` `hexagonalNum(n)` `{` ` ` `return` `n * (2 * n - 1);` `}` `// Driver Code` `var` `n = 10;` `document.write(` `"10th Hexagonal number is = "` `+` ` ` `hexagonalNum(n));` `// This code is contributed by Kirti` ` ` `</script>` |

**Output: **

10th Hexagonal Number is = 190

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

This article is contributed by **Nishant_Singh(pintu)**. 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 GeeksforGeek’s main page and help other Geeks.

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