居中的十九边形数

给定一个数 n，找出第n 个中心化的十九边形数。
一个居中的十九边形数表示连续的十九边形（19 边多边形）层中中心的一个点和围绕它的其他点。

center_nonadecagonalnum

前几个居中的十九边形数是：
1、20、58、115、191、286、400、533、685、856、1046、1255…………………………
例子：

Input :  3
Output : 58 

Input : 13
Output :1483

在数学中，第 n项的中心十九边形数由下式给出：

$CN_{n}= (19n^2 - 19n +2)/2$

下面是上述想法的基本实现：

C++

// C++ Program to find
// nth centered
// nonadecagonal number
#include 
using namespace std;
 
// centered nonadecagonal
//  function
int center_nonadecagon_num( long int n )
{
    // Formula to calculate nth
    // centered nonadecagonal number
    return (19 * n * n - 19 * n + 2) / 2;
}
 
// Driver Code
int main()
{
    long int n = 2;
    cout << n << "th centered nonadecagonal number : "
                   << center_nonadecagon_num(n);
    cout << endl;
    n = 7;
    cout << n << "th centered nonadecagonal number : "
                  << center_nonadecagon_num(n);
 
    return 0;
}

Java

// Java Program to find nth centered
// nonadecagonal number
import java.io.*;
 
class GFG {
     
    // centered nonadecagonal
    // function
    static int center_nonadecagon_num(int n)
    {
        // Formula to calculate nth
        // centered nonadecagonal number
        return (19 * n * n - 19 * n + 2) / 2;
    }
     
    // Driver code
    public static void main (String[] args)
    {
        int n = 2;
        System.out.print ( n + "th centered "
                + "nonadecagonal number : ");
        System.out.println (
                   center_nonadecagon_num(n));
     
        n = 7;
        System.out.print ( n + "th centered "
                + "nonadecagonal number : ");
        System.out.println(
                  center_nonadecagon_num(n));
    }
}
 
// This code is contributed by m_kit

Python3

# Program to find nth
# centered nonadecagonal number
def center_nonadecagon_num(n) :
     
    # Formula to calculate
    # nth centered nonadecagonal
    # number & return it into
    # main function.
     
    return (19 * n * n -
            19 * n + 2) // 2
 
# Driver Code
if __name__ == '__main__' :
         
    n = 2
    print(n,"nd centered nonadecagonal " +
                              "number : ",
                center_nonadecagon_num(n))
 
    n = 7
    print(n,"nd centered nonadecagonal " +
                              "number : ",
                center_nonadecagon_num(n))
 
# This code is contributed by ajit

C#

// C# Program to find
// nth centered
// nonadecagonal number
using System;
 
class GFG
{
     
    // centered nonadecagonal
    // function
    static int center_nonadecagon_num(int n)
    {
        // Formula to calculate nth
        // centered nonadecagonal number
        return (19 * n * n -
                19 * n + 2) / 2;
    }
     
    // Driver code
    static public void Main ()
    {
         
        int n = 2;
        Console.Write ( n + "th centered " +
                 "nonadecagonal number : ");
        Console.WriteLine(
                 center_nonadecagon_num(n));
     
        n = 7;
        Console.Write( n + "th centered " +
                "nonadecagonal number : ");
        Console.WriteLine(
                center_nonadecagon_num(n));
    }
}
 
// This code is contributed by ajit

PHP

Javascript

输出：

2th centered nonadecagonal number : 20
7th centered nonadecagonal numbe : 400

时间复杂度： O(1)
辅助空间： O(1)

参考：
http://oeis.org/A069132

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