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Hexagonal Number
  • Difficulty Level : Basic
  • Last Updated : 27 May, 2020

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 Hn = 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.

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