中心二十面体编号程序

给定一个数字n，我们需要找到第n个居中的二十面体数。
说明：居中的二十面体编号是代表二十面体的居中图形编号。
居中的二十面体数字序列的前几个是：
1，13，55，147，309，561，923，1415，2057，2869，3871，5083，6525，8217………………。
第n个中心二十面体数的数学公式：

$\begin{math}CI_{n} = \frac{(2n+1)(5n^2+5n+3)}{3}$

例子 ：

Input : n = 4
Output : 309

Input : n = 12
Output : 6525

下面是上面公式的实现

C++

// C++ Program to find nth
// Centered icosahedral number
#include 
using namespace std;
 
// Function to find
// Centered icosahedral number
int centeredIcosahedralNum(int n)
{
    // Formula to calculate nth
    // Centered icosahedral number
    // and return it into main function.
    return (2 * n + 1) * (5 * n * n + 5 * n + 3) / 3;
}
 
// Driver Code
int main()
{
    int n = 10;
    cout << centeredIcosahedralNum(n) << endl;
 
    n = 12;
    cout << centeredIcosahedralNum(n) << endl;
 
    return 0;
}

Java

// Java Program to find nth
// Centered icosahedral number
// Java Program to find nth Centered
// icosahedral number
 
import java.io.*;
 
class GFG {
     
    // Function to find Centered
    // icosahedral number
    static int centeredIcosahedralNum(int n)
    {
         
        // Formula to calculate nth Centered
        // icosahedral number and return it
        // into main function.
        return (2 * n + 1) * (5 * n * n +
                             5 * n + 3) / 3;
    }
     
    // Driver Code
    public static void main (String[] args)
    {
        int n = 10;
        System.out.println(
                   centeredIcosahedralNum(n));
     
        n = 12;
        System.out.println(
                   centeredIcosahedralNum(n));
    }
}
 
// This code is contributed by anuj_67.

Python3

# Python program to find nth
# Centered icosahedral number
 
# Function to calculate
# Centered icosahedral number
 
def centeredIcosahedralNum(n):
 
    # Formula to calculate nth
    # Centered icosahedral number
    return ((2 * n + 1) *
            (5 * n * n + 5 * n + 3) // 3)
 
# Driver Code
n = 10
print(centeredIcosahedralNum(n))
 
n = 12
print(centeredIcosahedralNum(n))
                     
# This code is contributed by ajit.

C#

// C# Program to find nth
// Centered icosahedral number
// Java Program to find nth Centered
// icosahedral number
 
using System;
 
class GFG {
     
    // Function to find Centered
    // icosahedral number
    static int centeredIcosahedralNum(int n)
    {
         
        // Formula to calculate nth Centered
        // icosahedral number and return it
        // into main function.
        return (2 * n + 1) * (5 * n * n +
                            5 * n + 3) / 3;
    }
     
    // Driver Code
    public static void Main ()
    {
        int n = 10;
        Console.WriteLine(
                centeredIcosahedralNum(n));
     
        n = 12;
        Console.WriteLine(
                centeredIcosahedralNum(n));
    }
}
 
// This code is contributed by anuj_67.

Javascript

 
// Javascript Program to find nth
// Centered icosahedral number
 
// Function to find
// Centered icosahedral number
function centeredIcosahedralNum(n)
{
 
    // Formula to calculate nth
    // Centered icosahedral number
    // and return it into main function.
    return parseInt((2 * n + 1) * (5 * n * n + 5 * n + 3) / 3);
}
 
// Driver Code
let n = 10;
document.write(centeredIcosahedralNum(n) + "<br>");
 
n = 12;
document.write(centeredIcosahedralNum(n));
 
// This code is contributed by souravmahato348.

输出 ：

3871
6525

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