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 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
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