七边形数

给定一个数N ，任务是找到^第N^个七边形数。

A Heptacontagon number is class of figurate number. It has 70 – sided polygon called heptacontagon. The N-th heptacontagon number count’s the 70 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few heptacontagonol numbers are 1, 70, 207, 412 … 
 

例子：

Input: N = 2 
Output: 70 
Explanation: 
The second heptacontagonol number is 70. 
Input: N = 3 
Output: 207 
 

方法：第N个七边形数由公式给出：

• s 边多边形的第 N 项 = $\frac{((s-2)n^2 - (s-4)n)}{2}$
• 因此 70 边多边形的第 N 项是

$Tn =\frac{((70-2)n^2 - (70-4)n)}{2} =\frac{(68n^2 - 66)}{2}$

下面是上述方法的实现：

C++

// C++ program for above approach
#include 
using namespace std;
 
// Finding the nth heptacontagon number
int heptacontagonNum(int n)
{
    return (68 * n * n - 66 * n) / 2;
}
 
// Driver code
int main()
{
    int N = 3;
     
    cout << "3rd heptacontagon Number is = "
         << heptacontagonNum(N);
 
    return 0;
}
 
// This code is contributed by shivanisinghss2110

C

// C program for above approach
#include 
#include 
 
// Finding the nth heptacontagon Number
int heptacontagonNum(int n)
{
    return (68 * n * n - 66 * n) / 2;
}
 
// Driver code
int main()
{
    int N = 3;
    printf("3rd heptacontagon Number is = %d",
           heptacontagonNum(N));
 
    return 0;
}

Java

// Java program for the above approach
class GFG{
 
// Finding the nth heptacontagon number
static int heptacontagonNum(int n)
{
    return (68 * n * n - 66 * n) / 2;
}
 
// Driver Code
public static void main(String[] args)
{
    int N = 3;
    System.out.println("3rd heptacontagon Number is = " +
                                    heptacontagonNum(N));
}
}
 
// This code is contributed by rutvik_56

Python3

# Python3 program for above approach
 
# Finding the nth heptacontagon Number
def heptacontagonNum(n):
 
    return (68 * n * n - 66 * n) // 2;
 
# Driver code
N = 3;
print("3rd heptacontagon Number is =",
                 heptacontagonNum(N));
 
# This code is contributed by Akanksha_Rai

C#

// C# program for the above approach
using System;
class GFG{
 
// Finding the nth heptacontagon number
static int heptacontagonNum(int n)
{
    return (68 * n * n - 66 * n) / 2;
}
 
// Driver Code
public static void Main()
{
    int N = 3;
    Console.Write("3rd heptacontagon Number is = " +
                               heptacontagonNum(N));
}
}
 
// This code is contributed by Akanksha_Rai

Javascript

 
// JavaScript program for above approach
 
// Finding the nth heptacontagon number
function heptacontagonNum(n)
{
    return (68 * n * n - 66 * n) / 2;
}
 
// Driver code
 
var N = 3;   
document.write("3rd heptacontagon Number is = " + heptacontagonNum(N));
 
 

输出：

3rd heptacontagon Number is = 207

时间复杂度： O(1)

辅助空间： O(1)

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

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