十边形数

给定数字n，任务是找到第n个十进制数。
十边形数字是将三角形和正方形数字的概念扩展到十边形(十一面多边形)的图形化数字。第n个十进制数计算n个嵌套十边形图案中的点数，它们全部共享一个公共角，其中该模式中的第i个十边形具有由i个点组成的边，这些点相互间隔一个单位。

例子：

Input : 2
Output :11

Input :6
Output :141

第n个十进制数的公式：

$\begin{math} H_{n}=((9n^2)-7n)/2 \end{math}$

C++

// C++ program to find nth
// Hendecagonal number
#include 
using namespace std;
  
// Function to find
// Hendecagonal number
int hendecagonal_num(int n)
{
    // Formula to calculate nth
    // Hendecagonal number
    return (9 * n * n - 7 * n) / 2;
}
  
// Driver Code
int main()
{
    int n = 3;
    cout << n << "rd Hendecagonal number: ";
    cout << hendecagonal_num(n);
    cout << endl;
    n = 10;
    cout << n << "th Hendecagonal number: ";
    cout << hendecagonal_num(n);
  
    return 0;
}

Java

// Java program to find nth
// Hendecagonal number
import java.io.*;
  
class GFG
{
      
// Function to find
// Hendecagonal number
static int hendecagonal_num(int n)
{
    // Formula to calculate nth
    // Hendecagonal number
    return (9 * n * n - 
            7 * n) / 2;
}
  
// Driver Code
public static void main (String[] args)
{
int n = 3;
System.out.print(n + "rd Hendecagonal " +
                             "number: ");
System.out.println(hendecagonal_num(n));
  
n = 10;
System.out.print(n + "th Hendecagonal " + 
                             "number: ");
System.out.println(hendecagonal_num(n));
}
}
  
// This code is contributed by ajit

Python3

# Program to find nth
# Hendecagonal number
  
# Function of Hendecagonal 
# number 
def hendecagonal_num(n) :
      
    # Formula to calculate nth
    # Hendecagonal number &
    # return it into main function.
      
    return (9 * n * n -
            7 * n) // 2
  
# Driver Code
if __name__ == '__main__' :
          
    n = 3
    print(n,"rd Hendecagonal number : " , 
                    hendecagonal_num(n))
  
    n = 10
    print(n,"th Hendecagonal number : " , 
                    hendecagonal_num(n))
  
# This code is contributed by ajit

C#

// C# program to find nth
// Hendecagonal number
using System;
  
class GFG
{
// Function to find
// Hendecagonal number
static int hendecagonal_num(int n)
{
    // Formula to calculate nth
    // Hendecagonal number
    return (9 * n * n - 7 * n) / 2;
}
  
// Driver Code
static public void Main ()
{
    int n = 3;
    Console.Write(n + 
                 "rd Hendecagonal number: ");
    Console.WriteLine( hendecagonal_num(n));
  
    n = 10;
    Console.Write(n + 
                 "th Hendecagonal number: ");
    Console.WriteLine( hendecagonal_num(n));
    }
}
  
// This code is contributed by aj_36

输出 ：

3th Hendecagonal number: 30
10th Hendecagonal number: 415

参考：https://en.wikipedia.org/wiki/Polygonal_number