八边形数

给定一个数字N ，任务是找到^第N^个八边形数字。

A Octacontagon numberr is class of figurate number. It has 80 – sided polygon called octacontagon. The N-th octacontagon number count’s the 80 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few octacontagonol numbers are 1, 80, 237, 472 … 
 

例子：

Input: N = 2 
Output: 80 
Explanation: 
The second octacontagonol number is 80. 
Input: N = 3 
Output: 237 
 

方法：第N个八边形数由公式给出：

• s 边多边形的第 N 项 = $\frac{((s-2)n^2 - (s-4)n)}{2}$
• 因此，80 边多边形的第 N 项是

$Tn =\frac{((80-2)n^2 - (80-4)n)}{2} =\frac{(78n^2 - 76n)}{2}$

下面是上述方法的实现：

C++

// C++ program for above approach
#include 
using namespace std;
 
// Finding the nth octacontagon Number
int octacontagonNum(int n)
{
    return (78 * n * n - 76 * n) / 2;
}
 
// Driver Code
int main()
{
    int n = 3;
    cout <<"3rd octacontagon Number is = "
         << octacontagonNum(n);
 
    return 0;
}
 
// This code is contributed by shivanisinghss2110

C

// C program for above approach
#include 
#include 
 
// Finding the nth octacontagon Number
int octacontagonNum(int n)
{
    return (78 * n * n - 76 * n) / 2;
}
 
// Driver program to test above function
int main()
{
    int n = 3;
    printf("3rd octacontagon Number is = %d",
           octacontagonNum(n));
 
    return 0;
}

Java

// Java program for above approach
import java.util.*;
class GFG{
 
// Finding the nth octacontagon Number
static int octacontagonNum(int n)
{
    return (78 * n * n - 76 * n) / 2;
}
 
// Driver Code
public static void main(String args[])
{
    int n = 3;
    System.out.print("3rd octacontagon Number is = " +
                                  octacontagonNum(n));
}
}
 
// This code is contributed by Akanksha_Rai

Python3

# Python3 program for above approach
 
# Finding the nth octacontagon number
def octacontagonNum(n):
 
    return (78 * n * n - 76 * n) // 2
 
# Driver code
n = 3
print("3rd octacontagon Number is = ",
                   octacontagonNum(n))
 
# This code is contributed by divyamohan123

C#

// C# program for above approach
using System;
class GFG{
 
// Finding the nth octacontagon Number
static int octacontagonNum(int n)
{
    return (78 * n * n - 76 * n) / 2;
}
 
// Driver Code
public static void Main()
{
    int n = 3;
    Console.Write("3rd octacontagon Number is = " +
                               octacontagonNum(n));
}
}
 
// This code is contributed by Akanksha_Rai

Javascript

 
// Javacript program for above approach
 
// Finding the nth octacontagon Number
function octacontagonNum(n)
{
    return (78 * n * n - 76 * n) / 2;
}
 
// Driver Code
var n = 3;
document.write("3rd octacontagon Number is = " + octacontagonNum(n));
 
 

输出：

3rd octacontagon Number is = 237

时间复杂度： O(1)

辅助空间： O(1)

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

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