# Tridecagonal Number

Given a number **N**, the task is to find the **N ^{th} 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 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 are1, 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 N^{th} tridecagonal number is given by the formula:

Below is the implementation of the above approach:

## C++

`// 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

`// 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

`# 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#

`// 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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