中心十二面体数

给定一个数 n，找出第n 个中心十二面体数。
中心十二面体数是具象数的一类。它由一个中心点组成，周围是连续的十二面体（具有 12 个平面的多面体）层。
前几个中心十二面体数（其中 n = 0、1、2、3……）是：
1, 33, 155, 427, 909, 1661 ……………
例子：

Input : 5
Output : 1661

Input :1
Output :33

第 n 个中心十二面体数的数学公式由下式给出：

$Cd_{n}=(2n+1)(5n^2+5n+1)$

下面是上述想法的基本实现：

C++

// Program to find nth centered
// dodecahedral number
#include 
using namespace std;
 
// Function to find
// centered dodecahedral number
int CenteredDodecahedral_num(long int n)
{
    // Formula to calculate nth
    // centered dodecahedral number
    // and return it into main function.
    return (2 * n + 1) * (5 * n * n + 5 * n + 1);
}
// Driver Code
int main()
{
    long int n = 3;
    // print result
    cout << n << "th Centered Dodecahedral number : ";
    cout << CenteredDodecahedral_num(n) << endl;
 
    n = 10;
    // print result
    cout << n << "th Centered Dodecahedral number : ";
    cout << CenteredDodecahedral_num(n);
 
    return 0;
}

Java

// Java Program to find nth
// centered dodecahedral number
import java.io.*;
 
class GFG {
 
    // Function to find centered
    // dodecahedral number
    static int CenteredDodecahedral_num(int n)
    {
         
        // Formula to calculate nth
        // centered dodecahedral number
        // and return it into main function.
         
        return (2 * n + 1) *
                     (5 * n * n + 5 * n + 1);
    }
     
    // Driver Code
    public static void main (String[] args)
    {
 
        int n = 3;
         
        // print result
        System.out.print( n + "th Centered "
                + "Dodecahedral number : ");
        System.out.println (
                CenteredDodecahedral_num(n));
 
        n = 10;
         
        // print result
        System.out.print( n + "th Centered "
                + "Dodecahedral number : ");
        System.out.println(
               CenteredDodecahedral_num(n));
    }
}
 
// This code is contributed by m_kit.

Python3

# Program to find nth centered
# dodecahedral number
 
# Function to find centered
# dodecahedral number
def CenteredDodecahedral_num(n) :
     
    # Formula to calculate nth
    # centered dodecahedral number
    return (2 * n + 1) * (5 * n * n + 5 * n + 1)
 
# Driver Code
if __name__ == '__main__' :
         
    n = 3
    print(n,"rd centered dodecahedral number: ",
                CenteredDodecahedral_num(n))
    n = 10
    print(n,"th centered dodecahedral number : ",
                CenteredDodecahedral_num(n))
                 
# This code is contributed by aj_36

C#

// C# Program to find
// nth centered
// dodecahedral number
using System;
 
class GFG
{
     
    // Function to find
    // nth centered
    // dodecahedral number
    static int CenteredDodecahedral_num(int n)
    {
         
        // Formula to calculate
        // nth centered dodecahedral
        // number and return it
        // into main function.
        return (2 * n + 1) *
               (5 * n * n +
                5 * n + 1);
    }
     
    // Driver Code
    static public void Main ()
    {
        int n = 3;
         
        // print result
        Console.Write( n + "th Centered " +
                 "Dodecahedral number : ");
        Console.WriteLine(
                CenteredDodecahedral_num(n));
 
        n = 10;
         
        // print result
        Console.Write( n + "th Centered " +
                 "Dodecahedral number : ");
        Console.WriteLine(
                CenteredDodecahedral_num(n));
    }
}
 
// This code is contributed by ajit

Javascript

 
// Javascript Program to find nth
// centered dodecahedral number
 
// Function to find centered
// dodecahedral number
function CenteredDodecahedral_num(n)
{
     
    // Formula to calculate nth
    // centered dodecahedral number
    // and return it into main function.
    return (2 * n + 1) *
           (5 * n * n + 5 * n + 1);
}
     
// Driver code
var n = 3;
         
// print result
document.write(n + "th Centered " +
               "Dodecahedral number : ");
document.write(CenteredDodecahedral_num(n) + "<br>");
 
n = 10;
 
// print result
document.write(n + "th Centered " +
               "Dodecahedral number : ");
document.write(CenteredDodecahedral_num(n));
 
// This code is contributed by Khushboogoyal499
 

输出 ：

3th Centered Dodecahedral number : 427
10th Centered Dodecahedral number : 11571

时间复杂度： O(1)
辅助空间： O(1)

参考：
https://en.wikipedia.org/wiki/Centered_dodecahedral_number

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