# Centered Hexadecagonal Number

Given a number n, find the** nth **Centered Hexadecagonal Number.

A **Centered Hexadecagonal number** represents a dot in the centre and other dots around it in successive hexadecagonal(16 sided polygon) layers.

The first few Centered Hexadecagonal numbers are:

1, 17, 49, 97, 161, 241, 337, 449, 577, 721, 881………………….

**Examples :**

Input : 3 Output : 49 Input : 10 Output : 721

In mathematics, Centered hexadecagonal number for the** n-th **term is given by :

Below is the basic implementation of the above idea:

## C++

`// C++ Program to find` `// nth centered hexadecagonal` `// number` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// centered hexadecagonal function` `int` `center_hexadecagonal_num(` `long` `int` `n)` `{` ` ` `// Formula to calculate nth` ` ` `// centered hexadecagonal number` ` ` `return` `8 * n * n - 8 * n + 1;` `}` `// Driver Code` `int` `main()` `{` ` ` `long` `int` `n = 2;` ` ` `cout << n << ` `"th centered hexadecagonal number : "` ` ` `<< center_hexadecagonal_num(n);` ` ` `cout << endl;` ` ` `n = 12;` ` ` `cout << n << ` `"th centered hexadecagonal numbe : "` ` ` `<< center_hexadecagonal_num(n);` ` ` `return` `0;` `}` |

## Java

`// Java Program to find nth` `// centered hexadecagonal number` `import` `java.io.*;` `class` `GFG` `{` ` ` `// centered hexadecagonal function` ` ` `static` `int` `center_hexadecagonal_num(` `int` `n)` ` ` `{` ` ` `// Formula to calculate nth` ` ` `// centered hexadecagonal number` ` ` `return` `8` `* n * n -` ` ` `8` `* n + ` `1` `;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `main(String args[])` ` ` `{` ` ` `int` `n = ` `2` `;` ` ` `System.out.print(n + ` `"th centered "` `+` ` ` `"hexadecagonal number: "` `);` ` ` `System.out.println(center_hexadecagonal_num(n));` ` ` ` ` `n = ` `12` `;` ` ` `System.out.print(n + ` `"th centered "` `+` ` ` `"hexadecagonal number: "` `);` ` ` `System.out.println(center_hexadecagonal_num(n));` ` ` `}` `}` `// This code is contributed by ajit.` |

## Python3

`# Program to find nth` `# centered hexadecagonal` `# number` `# centered hexadecagonal` `# function` `def` `center_hexadecagonal_num(n):` ` ` ` ` `# Formula to calculate` ` ` `# nth centered hexadecagonal` ` ` `# number` ` ` `return` `8` `*` `n ` `*` `n ` `-` `8` `*` `n ` `+` `1` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` `n ` `=` `2` ` ` `print` `(n,` `"nd centered hexadecagonal "` `+` ` ` `"number : "` `,` ` ` `center_hexadecagonal_num(n))` ` ` `n ` `=` `12` ` ` `print` `(n,` `"th centered hexadecagonal "` `+` ` ` `"number : "` `,` ` ` `center_hexadecagonal_num(n))` ` ` `# This code is contributed` `# by akt_mit` |

## C#

`// C# Program to find nth` `// centered hexadecagonal number` `using` `System;` `class` `GFG` `{` ` ` ` ` `// centered hexadecagonal` ` ` `// function` ` ` `static` `int` `center_hexadecagonal_num(` `int` `n)` ` ` `{` ` ` `// Formula to calculate nth` ` ` `// centered hexadecagonal number` ` ` `return` `8 * n * n -` ` ` `8 * n + 1;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `static` `public` `void` `Main ()` ` ` `{` ` ` `int` `n = 2;` ` ` `Console.Write(n + ` `"th centered "` `+` ` ` `"hexadecagonal number: "` `);` ` ` `Console.WriteLine(center_hexadecagonal_num(n));` ` ` ` ` `n = 12;` ` ` `Console.Write(n + ` `"th centered "` `+` ` ` `"hexadecagonal number: "` `);` ` ` `Console.WriteLine(center_hexadecagonal_num(n));` ` ` `}` `}` `// This code is contributed by m_kit` |

## PHP

`<?php` `// PHP Program to find` `// nth centered hexadecagonal` `// number` `// centered hexadecagonal function` `function` `center_hexadecagonal_num(` `$n` `)` `{` ` ` `// Formula to calculate nth` ` ` `// centered hexadecagonal number` ` ` `return` `8 * ` `$n` `* ` `$n` `- 8 * ` `$n` `+ 1;` `}` `// Driver Code` `$n` `= 2;` `echo` `$n` `, ` `"th centered hexadecagonal number : "` `,` ` ` `center_hexadecagonal_num(` `$n` `);` `echo` `"\n"` `;` `$n` `= 12;` `echo` `$n` `, ` `"th centered hexadecagonal numbe : "` `,` ` ` `center_hexadecagonal_num(` `$n` `);` `// This code is contributed by ajit` `?>` |

## Javascript

`<script>` `// Javascript Program to find nth` `// centered hexadecagonal number` `// Centered hexadecagonal function` `function` `center_hexadecagonal_num(n)` `{` ` ` ` ` `// Formula to calculate nth` ` ` `// centered hexadecagonal number` ` ` `return` `8 * n * n - 8 * n + 1;` `}` `// Driver code` `var` `n = 2;` `document.write(n + ` `"th centered "` `+` ` ` `"hexadecagonal number: "` `);` `document.write(center_hexadecagonal_num(n) + ` `"<br>"` `);` `n = 12;` `document.write(n + ` `"th centered "` `+` ` ` `"hexadecagonal number: "` `);` `document.write(center_hexadecagonal_num(n));` `// This code is contributed by Ankita saini` `</script>` |

**Output :**

2th centered hexadecagonal number : 17 12th centered hexadecagonal numbe : 1057

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

References:

http://oeis.org/A069129

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