六角数

给定整数n，任务是找到第n个六角形数。第n个六边形数字Hn是由正六边形的轮廓组成的点阵图案中不同点的数量，这些正六边形的轮廓在重叠六边形以共享一个顶点时最多可包含n个点。{Source：wiki}

Input: n = 2
Output: 6

Input: n = 5
Output: 45

Input: n = 7
Output: 91

通常，多边形数(三角形数，平方数等)是表示为以规则多边形的形状排列的点或小卵石的数字。前几个五边形数字是1、5、12等。
如果s是多边形中的边数，则第n个s角数P(s，n)的公式为

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 
#include 
 
// 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.

Javascript

 
// 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
     

输出：

10th Hexagonal Number is =  190