居中八面体数

给定一个数字n，我们需要找到第n个居中的八面体数。
说明：居中的八面体数字是图形数字。它计算位于以原点为中心的八面体内部的三维整数晶格的点数。相同的数字是Delannoy数的特殊情况，它计算某些二维晶格路径。
第几个居中的八面体数(其中n = 0、1、2、3…。)是：
1，7，25，63，129，231，377，575，833，1159…………………………。
第n个居中八面体数的数学公式：

$\begin{math}Co_{n} = \frac{(2n+1)(2n^2+2n+3)}{3}$

例子 ：

Input : n = 6
Output : 377

Input : n = 15
Output : 4991

C++

// C++ Program to find nth
// Centered octahedral number
#include 
using namespace std;
 
// Function to find
// Centered octahedral number
 
int centeredOctahedral(int n)
{
    // Formula to calculate nth
    // Centered octahedral number
    // and return it into main function.
    return (2 * n + 1) * (2 * n * n + 2 * n + 3) / 3;
}
 
// Driver Code
int main()
{
    int n = 3;
    cout << centeredOctahedral(n) << endl;
 
    n = 9;
    cout << centeredOctahedral(n) << endl;
 
    return 0;
}

Java

// Java Program to find nth
// Centered octahedral number
import java.io.*;
 
class GFG
{
    // Function to find
    // Centered octahedral number
    static int centeredOctahedral(int n)
    {
         
    // Formula to calculate nth
    // Centered octahedral number
    // and return it into main function.
     
    return (2 * n + 1) *
           (2 * n * n + 2 * n + 3) / 3;
    }
 
    // Driver Code
    public static void main (String[] args)
    {
    int n = 3;
    System.out.print( centeredOctahedral(n));
    System.out.println();
    n = 9;
    System.out.print(centeredOctahedral(n));
    }
}
 
// This code is contributed by aj_36

Python3

# Python 3 Program to find nth
# Centered octahedral number
 
# Centered octahedral
# number function
def centeredOctahedral(n) :
     
    # Formula to calculate nth
    # Centered octahedral number
    # return it into main function.
    return (2 * n + 1) * (
            2 * n * n +
            2 * n + 3) // 3
 
# Driver Code
if __name__ == '__main__' :
         
    n = 3
    print(centeredOctahedral(n))
    n = 9
    print(centeredOctahedral(n))
 
# This code is contributed ajit

C#

// C# Program to find nth
// Centered octahedral number
using System;
 
public class GFG {
     
    // Function to find
    // Centered octahedral number
    static int centeredOctahedral(int n)
    {
         
        // Formula to calculate nth
        // Centered octahedral number
        // and return it into main function.
         
        return (2 * n + 1) *
            (2 * n * n + 2 * n + 3) / 3;
    }
 
    // Driver Code
    static public void Main ()
    {
        int n = 3;
        Console.WriteLine(
               centeredOctahedral(n));
 
        n = 9;
        Console.WriteLine(
              centeredOctahedral(n));
    }
}
 
// This code is contributed by m_kit.

Javascript

 
// Javascript Program to find nth
// Centered octahedral number
 
// Function to find
// Centered octahedral number
function centeredOctahedral(n)
{
     
    // Formula to calculate nth
    // Centered octahedral number
    // and return it into main function.
     
    return (2 * n + 1) *
           (2 * n * n + 2 * n + 3) / 3;
}
 
 
// Driver Code
 
var n = 3;
document.write(centeredOctahedral(n));
document.write("<br>");
 
n = 9;
document.write(centeredOctahedral(n));
 
// This code is contributed by Kirti
     

输出 ：

63
1159

参考：
https://zh.wikipedia.org/wiki/Centered_octahedral_number