中心四面体数

给定整数n，我们需要找到第n个居中的四面体数。
说明：中心四面体数是代表四面体的中心比喻数。
四面体数：如果一个数字可以表示为具有三角形底面和三边的金字塔，则称为四面体，称为四面体。第n个四面体数是前n个三角数之和。
前几个居中的四面体数系列是：
1，5，15，35，69，121，195，295，425，589…………………………。
中心四面体数的数学n项：

$\\ CTh_{n} = \frac{(2n+1)(n^2+n+3)}{3}$

例子 ：

Input : n = 3
Output : 35

Input : n = 9
Output : 589

下面是上述公式的实现。

C++

// C++ Program to find nth
// Centered tetrahedral number
#include 
using namespace std;
 
// Function to find centered
// Centered tetrahedral number
int centeredTetrahedralNumber(int n)
{
    // Formula to calculate nth
    // Centered tetrahedral number
    // and return it into main function.
    return (2 * n + 1) * (n * n + n + 3) / 3;
}
 
// Driver Code
int main()
{
    int n = 6;
 
    cout << centeredTetrahedralNumber(n);
 
    return 0;
}

Java

// Java Program to find nth Centered
// tetrahedral number
import java.io.*;
 
class GFG {
 
    // Function to find centered
    // Centered tetrahedral number
    static int centeredTetrahedralNumber(int n)
    {
         
        // Formula to calculate nth
        // Centered tetrahedral number
        // and return it into main function.
        return (2 * n + 1) * (n * n + n + 3) / 3;
    }
     
    // Driver Code
 
 
    public static void main (String[] args)
    {
        int n = 6;
 
        System.out.println(
                   centeredTetrahedralNumber(n));
    }
}
 
// This code is contributed by anuj_67.

Python3

# Python program to find nth
# Centered tetrahedral number
 
# Function to calculate
# Centered tetrahedral number
 
def centeredTetrahedralNumber(n):
 
    # Formula to calculate nth
    # Centered tetrahedral number
    # and return it into main function
     
    return (2 * n + 1) * (n * n + n + 3) // 3
 
# Driver Code
n = 6
print(centeredTetrahedralNumber(n))
                     
# This code is contributed by ajit

C#

// C# Program to find nth Centered
// tetrahedral number
using System;
 
class GFG {
 
    // Function to find centered
    // Centered tetrahedral number
    static int centeredTetrahedralNumber(int n)
    {
         
        // Formula to calculate nth
        // Centered tetrahedral number
        // and return it into main function.
        return (2 * n + 1) * (n * n + n + 3) / 3;
    }
     
    // Driver Code
 
 
    public static void Main ()
    {
        int n = 6;
 
        Console.WriteLine(
                centeredTetrahedralNumber(n));
    }
}
 
// This code is contributed by anuj_67.

Javascript

 
// Javascript program to find nth Centered
// tetrahedral number
 
// Function to find centered
// Centered tetrahedral number
function centeredTetrahedralNumber(n)
{
     
    // Formula to calculate nth
    // Centered tetrahedral number
    // and return it into main function.
    return (2 * n + 1) * (n * n + n + 3) / 3;
}
 
// Driver Code
 
// Given Number
var n = 6;
 
document.write(centeredTetrahedralNumber(n));
 
// This code is contributed by Kirti
     

输出 ：

195