中心十六进制数

给定数字n，找到第n个中心十六进制数。
中心六边形数字表示连续的十六边形(16面多边形)层中位于中心的点和其周围的其他点。

前几个居中六边形数字是：
1、17、49、97、161、241、337、449、577、721、881……………………。

例子 ：

Input :  3
Output : 49

Input : 10
Output : 721

在数学中，第n个项的居中十六进制数由下式给出：

$CH_{n}= 8n^2 -8n+1$

以下是上述想法的基本实现：

C++

// C++ Program to find
// nth centered hexadecagonal
// number
#include 
using namespace std;
 
// centered hexadecagonal function
int center_hexadecagonal_num(long int n)
{
    // Formula to calculate nth
    // centered hexadecagonal number
    return 8 * n * n - 8 * n + 1;
}
 
// Driver Code
int main()
{
    long int n = 2;
    cout << n << "th centered hexadecagonal number : "
                    << center_hexadecagonal_num(n);
    cout << endl;
    n = 12;
    cout << n << "th centered hexadecagonal numbe : "
                    << center_hexadecagonal_num(n);
 
    return 0;
}

Java

// Java Program to find nth
// centered hexadecagonal number
import java.io.*;
 
class GFG
{
    // centered hexadecagonal function
    static int center_hexadecagonal_num(int n)
    {
        // Formula to calculate nth
        // centered hexadecagonal number
        return 8 * n * n -
               8 * n + 1;
    }
     
    // Driver Code
    public static void main(String args[])
    {
        int n = 2;
        System.out.print(n + "th centered " +
                    "hexadecagonal number: ");
        System.out.println(center_hexadecagonal_num(n));
         
        n = 12;
        System.out.print(n + "th centered " +
                    "hexadecagonal number: ");
        System.out.println(center_hexadecagonal_num(n));
    }
}
 
// This code is contributed by ajit.

Python3

# Program to find nth
# centered hexadecagonal
# number
 
# centered hexadecagonal
# function
def center_hexadecagonal_num(n):
     
    # Formula to calculate
    # nth centered hexadecagonal
    # number
    return 8 * n * n - 8 * n + 1
 
# Driver Code
if __name__ == '__main__' :
         
    n = 2
    print(n,"nd centered hexadecagonal " +
                              "number : ",
              center_hexadecagonal_num(n))
    n = 12
    print(n,"th centered hexadecagonal " +
                              "number : ",
              center_hexadecagonal_num(n))
                 
# This code is contributed
# by akt_mit

C#

// C# Program to find nth
// centered hexadecagonal number
using System;
 
class GFG
{
     
    // centered hexadecagonal
    // function
    static int center_hexadecagonal_num(int n)
    {
        // Formula to calculate nth
        // centered hexadecagonal number
        return 8 * n * n -
               8 * n + 1;
    }
     
    // Driver Code
    static public void Main ()
    {
        int n = 2;
        Console.Write(n + "th centered " +
                    "hexadecagonal number: ");
        Console.WriteLine(center_hexadecagonal_num(n));
         
        n = 12;
        Console.Write(n + "th centered " +
                    "hexadecagonal number: ");
        Console.WriteLine(center_hexadecagonal_num(n));
    }
}
 
// This code is contributed by m_kit

Javascript

 
// Javascript Program to find nth
// centered hexadecagonal number
 
// Centered hexadecagonal function
function center_hexadecagonal_num(n)
{
     
    // Formula to calculate nth
    // centered hexadecagonal number
    return 8 * n * n - 8 * n + 1;
}
 
// Driver code
var n = 2;
document.write(n + "th centered " +
               "hexadecagonal number: ");
document.write(center_hexadecagonal_num(n) + "<br>");
 
n = 12;
document.write(n + "th centered " +
               "hexadecagonal number: ");
document.write(center_hexadecagonal_num(n));
 
 
// This code is contributed by Ankita saini
 

输出 ：

2th centered hexadecagonal number : 17
12th centered hexadecagonal numbe : 1057

参考：
http://oeis.org/A069129