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Hexagonal Number

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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++ program for above approach
#include<bits/stdc++.h>
using namespace std;
  
// 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;
    cout << "10th Hexagonal Number is "<< hexagonalNum(n) << endl;
    return 0;
}
 
// The code is contributed by Gautam goel (gautamgoel962)


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));
    }
}


Python3




# 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

Time complexity: O(1) since performing constant operations

Auxiliary space: O(1) since it is using constant variables

Reference:https://en.wikipedia.org/wiki/Hexagonal_number
See your article appearing on the GeeksforGeek’s main page and help other Geeks.

 



Last Updated : 01 Sep, 2022
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