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++

`// 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. ` `?> ` |

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.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready.