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 Numberint hexagonalNum(int n){ return n*(2*n - 1);}// Driver program to test above functionint 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 Numberint hexagonalNum(int n){ return n*(2*n - 1);}// Driver program to test above functionint main(){ int n = 10; printf("10th Hexagonal Number is = %d", hexagonalNum(n)); return 0;} |
Java
// Java program for above approachclass 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 numbersdef hexagonalNum( n ): return n*(2*n - 1)# Driver coden = 10print ("10th Hexagonal Number is = ", hexagonalNum(n)) |
C#
// C# program for above approachusing 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 Numberfunction 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 functionfunction 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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