中心五角形数

给定数字n，找到第n个中心五角形数。
中心五角形数代表连续的五角形(15面多边形)层中位于中心的点和围绕其的其他点。

例子 ：

Input :  2
Output : 16

Input : 8
Output : 421

五边形对数的第n个项：-

$PD_{n}= (15n^2 -15n+2)/2$

以下是上述想法的基本实现。

C++

// C++ Program to find
// nth centered
// pentadecagonal  number
#include 
using namespace std;
 
// centered pentadecagonal function
int center_pentadecagonal_num(long int n)
{
    // Formula to calculate nth
    // centered pentadecagonal number
    return (15 * n * n - 15 * n + 2) / 2;
}
 
// Driver Code
int main()
{
    long int n = 3;
    cout << n << "th number : "
             << center_pentadecagonal_num(n);
    cout << endl;
    n = 10;
    cout << n << "th number : "
             << center_pentadecagonal_num(n);
 
    return 0;
}

Java

// Java Program to find nth centered
// pentadecagonal number
 
import java.io.*;
 
class GFG {
     
    // centered pentadecagonal function
    static long center_pentadecagonal_num(long n)
    {
     
        // Formula to calculate nth
        // centered pentadecagonal number
        return (15 * n * n - 15 * n + 2) / 2;
    }
     
    // Driver Code
    public static void main (String[] args)
    {
     
        long n = 3;
        System.out.print(n + "th number : ");
        System.out.println(
                  center_pentadecagonal_num(n));
         
        n = 10;
        System.out.print( n + "th number : ");
        System.out.println(
                 center_pentadecagonal_num(n));
    }
}
 
// This code is contributed by ajit.

Python3

# Program to find nth
#centered pentadecagonal number
 
def center_pentadecagonal_num(n) :
     
    # Formula to calculate nth
    # centered pentadecagonal number
    return (15 * n * n - 15 * n + 2) // 2
 
# Driver Code
if __name__ == '__main__' :
         
    n = 3
    print(n,"rd number : ",
                center_pentadecagonal_num(n))
    n = 10
    print(n,"th number : ",
                 center_pentadecagonal_num(n))
                  
 
# This code is contributed  by m_kit

C#

// C# Program to find
// nth centered
// pentadecagonal number
using System;
 
class GFG
{
     
    // centered
    // pentadecagonal function
    static long center_pentadecagonal_num(long n)
    {
     
        // Formula to calculate
        // nth centered
        // pentadecagonal number
        return (15 * n * n -
                15 * n + 2) / 2;
    }
     
    // Driver Code
    static public void Main ()
    {
        long n = 3;
        Console.Write(n + "th number : ");
        Console.WriteLine(
                center_pentadecagonal_num(n));
         
        n = 10;
        Console.Write( n + "th number : ");
        Console.WriteLine(
                center_pentadecagonal_num(n));
    }
}
 
// This code is contributed by ajit.

Javascript

 
// Javascript program to find nth centered
// pentadecagonal number
 
// centered pentadecagonal function
function center_pentadecagonal_num(n)
{
     
    // Formula to calculate nth
    // centered pentadecagonal number
    return (15 * n * n - 15 * n + 2) / 2;
}
 
// Driver Code
var n = 3;
document.write(n + "th number : ");
document.write(center_pentadecagonal_num(n) + "<br>");
 
n = 10;
document.write( n + "th number : ");
document.write(center_pentadecagonal_num(n));
                  
// This code is contributed by Kirti
     

输出 ：

3th number : 46
10th number : 676