# Hexagonal Number

Given an integer n, the task is to find the n’th hexagonal number . The n’th 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; ` `} ` |

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## 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)); ` ` ` `} ` `} ` |

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## Python

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

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## 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. ` |

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## 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. ` `?> ` |

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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 GeeksforGeeks main page and help other Geeks.

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