# Icosihenagonal Number

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

An Icosihenagonal number is class of figurate number. It has 21 – sided polygon called Icosihenagon. The n-th Icosihenagonal number counts the 21 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few Icosihenagonal numbers are

1, 21, 60, 118, 195, 291, 406 …

**Examples:**

Input:N = 2Output:21Explanation:

The second Icosihenagonal number is 21Input:N = 6Output:291

**Approach:** In mathematics, the N^{th} Icosihenagonal number is given by the formula:

Below is the implementation of the above approach:

## C++

`// C++ program to find nth` `// Icosihenagonal number` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find` `// Icosihenagonal number` `int` `Icosihenagonal_num(` `int` `n)` `{` ` ` `// Formula to calculate nth` ` ` `// Icosihenagonal number` ` ` `return` `(19 * n * n - 17 * n) / 2;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 3;` ` ` `cout << Icosihenagonal_num(n) << endl;` ` ` `n = 10;` ` ` `cout << Icosihenagonal_num(n) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java program to find nth` `// Icosihenagonal number` `class` `GFG{` `// Function to find` `// Icosihenagonal number` `static` `int` `Icosihenagonal_num(` `int` `n)` `{` ` ` `// Formula to calculate nth` ` ` `// Icosihenagonal number` ` ` `return` `(` `19` `* n * n - ` `17` `* n) / ` `2` `;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `n = ` `3` `;` ` ` `System.out.print(Icosihenagonal_num(n) + ` `"\n"` `);` ` ` `n = ` `10` `;` ` ` `System.out.print(Icosihenagonal_num(n) + ` `"\n"` `);` `}` `}` `// This code is contributed by Rajput-Ji` |

## Python3

`# Python3 program to find nth` `# icosihenagonal number` `# Function to find` `# icosihenagonal number` `def` `Icosihenagonal_num(n):` ` ` ` ` `# Formula to calculate nth` ` ` `# icosihenagonal number` ` ` `return` `(` `19` `*` `n ` `*` `n ` `-` `17` `*` `n) ` `/` `2` ` ` `# Driver Code` `n ` `=` `3` `print` `(` `int` `(Icosihenagonal_num(n)))` `n ` `=` `10` `print` `(` `int` `(Icosihenagonal_num(n)))` `# This code is contributed by divyeshrabadiya07` |

## C#

`// C# program to find nth` `// Icosihenagonal number` `using` `System;` `class` `GFG{` `// Function to find` `// Icosihenagonal number` `static` `int` `Icosihenagonal_num(` `int` `n)` `{` ` ` `// Formula to calculate nth` ` ` `// Icosihenagonal number` ` ` `return` `(19 * n * n - 17 * n) / 2;` `}` `// Driver Code` `public` `static` `void` `Main()` `{` ` ` `int` `n = 3;` ` ` `Console.Write(Icosihenagonal_num(n) + ` `"\n"` `);` ` ` `n = 10;` ` ` `Console.Write(Icosihenagonal_num(n) + ` `"\n"` `);` `}` `}` `// This code is contributed by Code_Mech` |

## Javascript

`<script>` ` ` `// Javascript program to find nth` ` ` `// Icosihenagonal number` ` ` ` ` `// Function to find` ` ` `// Icosihenagonal number` ` ` `function` `Icosihenagonal_num(n)` ` ` `{` ` ` `// Formula to calculate nth` ` ` `// Icosihenagonal number` ` ` `return` `(19 * n * n - 17 * n) / 2;` ` ` `}` ` ` ` ` `let n = 3;` ` ` `document.write(Icosihenagonal_num(n) + ` `"</br>"` `);` ` ` ` ` `n = 10;` ` ` `document.write(Icosihenagonal_num(n));` ` ` `</script>` |

**Output:**

60 865

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

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