十三边形数

给定一个数N ，任务是找到第N^个十三边形数。

A tridecagonal number is a figurate number that extends the concept of triangular and square numbers to the tridecagon(a thirteen-sided polygon). The N^th tridecagonal number counts the number of dots in a pattern of N nested tridecagons, all sharing a common corner, where the ith tridecagon in the pattern has sides made of ‘i’ dots spaced one unit apart from each other. The first few tridecagonal numbers are 1, 13, 36, 70, 115, 171 … 
 

例子：

Input: N = 2 
Output: 13 
Explanation: 
The second tridecagonal number is 13.
Input: N = 6 
Output: 171 
 

方法：第N^个十三边形数由以下公式给出：

$Tn = (11n^2 - 9n)/2$

下面是上述方法的实现：

C++

// C++ program to find N-th
// Tridecagonal number
 
#include 
using namespace std;
 
// Function to find N-th
// Tridecagonal number
int Tridecagonal_num(int n)
{
    // Formula to calculate nth
    // Tridecagonal number
    return (11 * n * n - 9 * n) / 2;
}
 
// Driver Code
int main()
{
    int n = 3;
    cout << Tridecagonal_num(n) << endl;
     
    n = 10;
 
    cout << Tridecagonal_num(n) << endl;
 
    return 0;
}

Java

// Java program to find N-th
// tridecagonal number
class GFG{
 
// Function to find N-th
// tridecagonal number
static int Tridecagonal_num(int n)
{
     
    // Formula to calculate nth
    // tridecagonal number
    return (11 * n * n - 9 * n) / 2;
}
 
// Driver Code
public static void main(String[] args)
{
    int n = 3;
    System.out.print(Tridecagonal_num(n) + "\n");
     
    n = 10;
    System.out.print(Tridecagonal_num(n) + "\n");
}
}
 
// This code is contributed by Princi Singh

Python3

# Python3 program to find N-th
# tridecagonal number
 
# Function to find N-th
# tridecagonal number
def Tridecagonal_num(n):
     
    # Formula to calculate nth
    # tridecagonal number
    return (11 * n * n - 9 * n) / 2
 
# Driver Code
n = 3
print(int(Tridecagonal_num(n)))
 
n = 10
print(int(Tridecagonal_num(n)))
 
# This code is contributed by divyeshrabadiya07

C#

// C# program to find N-th
// tridecagonal number
using System;
 
class GFG{
 
// Function to find N-th
// tridecagonal number
static int Tridecagonal_num(int n)
{
     
    // Formula to calculate nth
    // tridecagonal number
    return (11 * n * n - 9 * n) / 2;
}
 
// Driver Code
public static void Main(String[] args)
{
    int n = 3;
    Console.Write(Tridecagonal_num(n) + "\n");
     
    n = 10;
    Console.Write(Tridecagonal_num(n) + "\n");
}
}
 
// This code is contributed by Rajput-Ji

Javascript

 
    // Javascript program to find N-th
    // Tridecagonal number
     
    // Function to find N-th
    // Tridecagonal number
    function Tridecagonal_num(n)
    {
        // Formula to calculate nth
        // Tridecagonal number
        return (11 * n * n - 9 * n) / 2;
    }
     
    let n = 3;
    document.write(Tridecagonal_num(n) + "</br>");
       
    n = 10;
   
    document.write(Tridecagonal_num(n));
     

输出：

36
505

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

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