Tridecagonal Number

Given a number N, the task is to find the Nth Tridecagonal number.

A tridecagonal number is a figurate number that extends the concept of triangular and square numbers to the tridecagon(a thirteen-sided polygon). The Nth 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 …

Examples:

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

Input: N = 6
Output: 171



Approach: The Nth tridecagonal number is given by the formula:

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

Below is the implementation of the above approach:

C++

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// C++ program to find N-th
// Tridecagonal number
  
#include <bits/stdc++.h>
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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output:

36
505

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

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