# Pentadecagonal Number

Given a number N, the task is to find the N^{th} Pentadecagonal number.

A Pentadecagonal number is a figurate number that extends the concept of triangular and square numbers to the pentadecagon(a 15-sided polygon). The N

^{th}pentadecagonal number counts the number of dots in a pattern of N nested pentadecagons, all sharing a common corner, where the i^{th}tridecagon in the pattern has sides made of ‘i’ dots spaced one unit apart from each other. The first few Pentadecagonal numbers are1, 15, 42, 82, 135, 201, 280 …

**Examples:**

Input:N = 2Output:15Explanation:

The second Pentadecagonal number is 15.Input:N = 6Output:201

**Approach:** The N^{th} Pentadecagonal number is given by the formula:

Below is the implementation of the above approach:

## C++

`// C++ program to find Nth` `// Pentadecagonal number` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find N-th` `// Pentadecagonal number` `int` `Pentadecagonal_num(` `int` `n)` `{` ` ` `// Formula to calculate nth` ` ` `// Pentadecagonal number` ` ` `return` `(13 * n * n - 11 * n) / 2;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `n = 3;` ` ` `cout << Pentadecagonal_num(n) << endl;` ` ` ` ` `n = 10;` ` ` `cout << Pentadecagonal_num(n) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java program to find Nth` `// pentadecagonal number` `import` `java.io.*;` `import` `java.util.*;` `class` `GFG{` ` ` `// Function to find N-th` `// pentadecagonal number` `static` `int` `Pentadecagonal_num(` `int` `n)` `{` ` ` ` ` `// Formula to calculate nth` ` ` `// Pentadecagonal number` ` ` `return` `(` `13` `* n * n - ` `11` `* n) / ` `2` `;` `}` ` ` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `n = ` `3` `;` ` ` `System.out.println(Pentadecagonal_num(n));` ` ` ` ` `n = ` `10` `;` ` ` `System.out.println(Pentadecagonal_num(n));` `}` `}` `// This code is contributed by coder001` |

## Python3

`# Python3 program to find Nth` `# pentadecagonal number` `# Function to find N-th` `# pentadecagonal number` `def` `Pentadecagonal_num(n):` ` ` ` ` `# Formula to calculate nth` ` ` `# pentadecagonal number` ` ` `return` `(` `13` `*` `n ` `*` `n ` `-` `11` `*` `n) ` `/` `2` `# Driver code ` `n ` `=` `3` `print` `(` `int` `(Pentadecagonal_num(n)))` `n ` `=` `10` `print` `(` `int` `(Pentadecagonal_num(n)))` `# This code is contributed by divyeshrabadiya07` |

## C#

`// C# program to find Nth` `// pentadecagonal number` `using` `System;` `class` `GFG{` ` ` `// Function to find N-th` `// pentadecagonal number` `static` `int` `Pentadecagonal_num(` `int` `n)` `{` ` ` ` ` `// Formula to calculate nth` ` ` `// Pentadecagonal number` ` ` `return` `(13 * n * n - 11 * n) / 2;` `}` ` ` `// Driver code` `public` `static` `void` `Main(` `string` `[] args)` `{` ` ` `int` `n = 3;` ` ` `Console.Write(Pentadecagonal_num(n) + ` `"\n"` `);` ` ` ` ` `n = 10;` ` ` `Console.Write(Pentadecagonal_num(n) + ` `"\n"` `);` `}` `}` `// This code is contributed by rutvik_56` |

## Javascript

`<script>` ` ` `// Javascript program to find Nth` ` ` `// Pentadecagonal number` ` ` ` ` `// Function to find N-th` ` ` `// Pentadecagonal number` ` ` `function` `Pentadecagonal_num(n)` ` ` `{` ` ` `// Formula to calculate nth` ` ` `// Pentadecagonal number` ` ` `return` `(13 * n * n - 11 * n) / 2;` ` ` `}` ` ` `let n = 3;` ` ` `document.write(Pentadecagonal_num(n) + ` `"</br>"` `);` ` ` ` ` `n = 10;` ` ` `document.write(Pentadecagonal_num(n));` ` ` `</script>` |

**Output:**

42 595

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

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