# Icosagonal number

Given a number n, the task is to find the nth Icosagonal number.

An Icosagonal number is the 20-gon is a twenty-sided polygon. The number derived from the figurative class. There are different pattern series number in this number. The dots are countable, arrange in a specific way of position and create a diagram. All the dots have a common dots points, all others dots are connected to this points and except this common point the dots connected to their i-th dots with their respective successive layer.**Examples :**

Input : 3

Output :57

Input :8

Output :512

Formula for nth icosagonal number:

## C++

`// C++ program to find` `// nth Icosagonal number` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to calculate Icosagonal number` `int` `icosagonal_poly(` `long` `int` `n)` `{` ` ` `// Formula for finding` ` ` `// nth Icosagonal number` ` ` `return` `(18 * n * n - 16 * n) / 2;` `}` `// Drivers code` `int` `main()` `{` ` ` `long` `int` `n = 7;` ` ` `cout << n << ` `"th Icosagonal number :"` ` ` `<< icosagonal_poly(n);` ` ` `return` `0;` `}` |

## Java

`// Java program to find` `// nth Icosagonal number` `import` `java.io.*;` `class` `GFG {` ` ` `// Function to calculate Icosagonal number` `static` `int` `icosagonal_poly(` `int` `n)` `{` ` ` `// Formula for finding` ` ` `// nth Icosagonal number` ` ` `return` `(` `18` `* n * n - ` `16` `* n) / ` `2` `;` `}` `// Drivers code` ` ` ` ` `public` `static` `void` `main (String[] args) {` ` ` ` ` `int` `n = ` `7` `;` ` ` ` ` `System.out.print (n + ` `"th Icosagonal number :"` `);` ` ` `System.out.println(icosagonal_poly(n));` ` ` `}` `}` `// This code is contributed by aj_36` |

## Python 3

`# Python 3 program to find` `# nth Icosagonal number` `# Function to calculate` `# Icosagonal number` `def` `icosagonal_poly(n) :` ` ` ` ` `# Formula for finding` ` ` `# nth Icosagonal number` ` ` `return` `(` `18` `*` `n ` `*` `n ` `-` ` ` `16` `*` `n) ` `/` `/` `2` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `n ` `=` `7` ` ` `print` `(n,` `"th Icosagonal number : "` `,` ` ` `icosagonal_poly(n))` `# This code is contributed m_kit` |

## C#

`// C# program to find` `// nth Icosagonal number` `using` `System;` `class` `GFG` `{` `// Function to calculate` `// Icosagonal number` `static` `int` `icosagonal_poly(` `int` `n)` `{` ` ` `// Formula for finding` ` ` `// nth Icosagonal number` ` ` `return` `(18 * n * n -` ` ` `16 * n) / 2;` `}` `// Driver code` `static` `public` `void` `Main ()` `{` ` ` `int` `n = 7;` `Console.Write(n + ` `"th Icosagonal "` `+` ` ` `"number :"` `);` `Console.WriteLine(icosagonal_poly(n));` `}` `}` `// This code is contributed by ajit` |

## PHP

`<?php` `// PHP program to find` `// nth Icosagonal number` `// Function to calculate` `// Icosagonal number` `function` `icosagonal_poly(` `$n` `)` `{` ` ` `// Formula for finding` ` ` `// nth Icosagonal number` ` ` `return` `(18 * ` `$n` `*` ` ` `$n` `- 16 * ` `$n` `) / 2;` `}` `// Driver Code` `$n` `= 7;` `echo` `$n` `, ` `"th Icosagonal number :"` `,` ` ` `icosagonal_poly(` `$n` `);` `// This code is contributed by ajit` `?>` |

## Javascript

`<script>` ` ` `// Javascript program to find nth Icosagonal number` ` ` ` ` `// Function to calculate` ` ` `// Icosagonal number` ` ` `function` `icosagonal_poly(n)` ` ` `{` ` ` `// Formula for finding` ` ` `// nth Icosagonal number` ` ` `return` `(18 * n * n - 16 * n) / 2;` ` ` `}` ` ` ` ` `let n = 7;` ` ` ` ` `document.write(n + ` `"th Icosagonal number :"` `);` ` ` `document.write(icosagonal_poly(n));` ` ` `</script>` |

**Output :**

7th Icosagonal number :385

**Time Complexity:** O(1)**Auxiliary Space:** O(1)

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

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**

In case you wish to attend **live classes **with experts, please refer **DSA Live Classes for Working Professionals **and **Competitive Programming Live for Students**.