中心八角数

给定一个数 n，找出第n 个居中的八边形数。
一个居中的八边形数代表一个八边形，在连续的八边形层中，一个点在中心，其他点围绕着中心点。

例子 ：

Input :  2
Output : 9

Input : 5
Output : 81

中心八边形第 n个数由下式给出：

$CO_{n}= 4n^2 -4n+1$

上述方法的基本实现：

C++

// Program to find nth
// centered octagonal
// number
#include 
using namespace std;
 
// Centered octagonal number function
int cen_octagonalnum(long int n)
{
    // Formula to calculate nth
    // centered octagonal number &
    // return it into main function.
    return (4 * n * n - 4 * n + 1);
}
 
// Driver Code
int main()
{
    long int n = 6;
    cout << n << "th  centered"
                 << " octagonal number : ";
    cout << cen_octagonalnum(n);
    cout << endl;
    n = 11;
    cout << n << "th  centered"
                  << " octagonal number : ";
    cout << cen_octagonalnum(n);
 
    return 0;
}

Java

// Java Program to find nth
// centered octagonal number
import java.io.*;
  
class GFG
{
      
    // Function to find centered
    // octagonal number
    static int centeredoctagonalNumber(int n)
    {
        // Formula to calculate nth
        // centered octagonal number
        // and return it into main function
        return 4 * n * (n - 1) + 1;
    }
      
    // Driver Code
    public static void main(String args[])
    {
        int n = 6;
        System.out.print(n + "th centered " +
                       "octagonal number: ");
        System.out.println(
                 centeredoctagonalNumber(n));
         
        n = 11;
        System.out.print(n + "th centered " +
                       "octagonal number: ");
        System.out.println(
                  centeredoctagonalNumber(n));
          
    }
}
 
// This code has been contributed by Prasad_Kshirsagar.

Python3

# Program to find nth
# centered octagonal number
 
def cen_octagonalnum(n) :
     
    # Formula to calculate nth
    # centered octagonal number
    return (4 * n * n -
            4 * n + 1)
 
# Driver Code
if __name__ == '__main__' :
         
    n = 6
    print(n,"th Centered",
            "octagonal number: ",
             cen_octagonalnum(n))
    n = 11
    print(n,"th Centered" ,
            "octagonal number: ",
             cen_octagonalnum(n))
                 
# This code is contributed
# by akt_mit

C#

// Program to find nth centered octagonal
// number
using System;
 
public class GFG{
     
    // Centered octagonal number function
    static long cen_octagonalnum(long  n)
    {
         
        // Formula to calculate nth
        // centered octagonal number &
        // return it into main function.
        return (4 * n * n - 4 * n + 1);
    }
     
    // Driver code
    static public void Main ()
    {
        long n = 6;
        Console.WriteLine(n + "th centered"
                    + " octagonal number : "
        + cen_octagonalnum(n));
     
        n = 11;
        Console.WriteLine(n + "th centered"
                    + " octagonal number : "
                    + cen_octagonalnum(n));
    }
}
 
// This code is contributed by anuj_67.

Javascript

 
// Javascript Program to find nth
// centered octagonal number
 
// Function to find centered
// octagonal number
function centeredoctagonalNumber(n)
{
     
    // Formula to calculate nth
    // centered octagonal number
    // and return it into main function
    return 4 * n * (n - 1) + 1;
}
 
// Driver Code
var n = 6;
document.write(n + "th centered " +
               "octagonal number: ");
document.write(centeredoctagonalNumber(n) + "<br>");
 
n = 11;
document.write(n + "th centered " +
               "octagonal number: ");
document.write(centeredoctagonalNumber(n));
          
// This code is contributed by Kirti
     

输出

6th  centered octagonal number : 121
11th  centered octagonal number : 441

时间复杂度： O(1)
辅助空间： O(1)