五角大楼编号

给定数字N ，任务是找到^第N^个五角大楼数。

A Pentacontagon number is class of figurate number. It has 50 – sided polygon called pentacontagon. The N-th pentacontagon number count’s the 50 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few pentacontagonol numbers are 1, 50, 147, 292 … 
 

例子：

Input: N = 2 
Output: 50 
Explanation: 
The second pentacontagonol number is 50. 
Input: N = 3 
Output: 147 
 

方法：第N个五角大楼数由以下公式给出：

• 侧多边形的第N个项= $\frac{((s-2)n^2 - (s-4)n)}{2}$
• 因此，第50个面多边形的第N个项是

$Tn =\frac{((50-2)n^2 - (50-4)n)}{2} =\frac{(48n^2 - 46)}{2}$

下面是上述方法的实现：

C++

// C++ program for above approach
#include 
using namespace std;
 
// Finding the nth pentacontagon Number
int pentacontagonNum(int n)
{
    return (48 * n * n - 46 * n) / 2;
}
 
// Driver Code
int main()
{
    int n = 3;
    cout << "3rd pentacontagon Number is = "
         << pentacontagonNum(n);
 
    return 0;
}
 
// This code is contributed by Akanksha_Rai

C

// C program for above approach
#include 
#include 
 
// Finding the nth pentacontagon Number
int pentacontagonNum(int n)
{
    return (48 * n * n - 46 * n) / 2;
}
 
// Driver program to test above function
int main()
{
    int n = 3;
    printf("3rd pentacontagon Number is = %d",
           pentacontagonNum(n));
 
    return 0;
}

Java

// Java program for above approach
import java.util.*;
 
class GFG {
 
// Finding the nth pentacontagon number
static int pentacontagonNum(int n)
{
    return (48 * n * n - 46 * n) / 2;
}
 
// Driver code
public static void main(String[] args)
{
    int n = 3;
     
    System.out.println("3rd pentacontagon Number is = " +
                                    pentacontagonNum(n));
}
}
 
// This code is contributed by offbeat

Python3

# Python3 program for above approach
 
# Finding the nth pentacontagon Number
def pentacontagonNum(n):
 
    return (48 * n * n - 46 * n) // 2
 
# Driver Code
n = 3
print("3rd pentacontagon Number is = ",
                   pentacontagonNum(n))
 
# This code is contributed by divyamohan123

C#

// C# program for above approach
using System;
 
class GFG {
 
// Finding the nth pentacontagon number
static int pentacontagonNum(int n)
{
    return (48 * n * n - 46 * n) / 2;
}
 
// Driver code
public static void Main(string[] args)
{
    int n = 3;
     
    Console.Write("3rd pentacontagon Number is = " +
                               pentacontagonNum(n));
}
}
 
// This code is contributed by rutvik_56

Javascript

 
// javascript program for above approach
 
// Finding the nth pentacontagon Number
function pentacontagonNum( n)
{
    return (48 * n * n - 46 * n) / 2;
}
 
// Driver code
let n = 3;
document.write("3rd pentacontagon Number is " + pentacontagonNum(n));
 
// This code contributed by gauravrajput1
 

输出：

3rd pentacontagon Number is = 147

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