# Centered nonadecagonal number

Given a number n, find the **nth **Centered Nonadecagonal number.

A **Centered Nonadecagonal Number** represents a dot in the centre and other dots surrounding it in successive nonadecagon(19 sided polygon) layers.

The first few Centered Nonadecagonal numbers are:

1, 20, 58, 115, 191, 286, 400, 533, 685, 856, 1046, 1255……………………………**Examples :**

Input : 3 Output : 58 Input : 13 Output :1483

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

Below is the basic implementation of the above idea:

## C++

`// C++ Program to find` `// nth centered` `// nonadecagonal number` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// centered nonadecagonal` `// function` `int` `center_nonadecagon_num( ` `long` `int` `n )` `{` ` ` `// Formula to calculate nth` ` ` `// centered nonadecagonal number` ` ` `return` `(19 * n * n - 19 * n + 2) / 2;` `}` `// Driver Code` `int` `main()` `{` ` ` `long` `int` `n = 2;` ` ` `cout << n << ` `"th centered nonadecagonal number : "` ` ` `<< center_nonadecagon_num(n);` ` ` `cout << endl;` ` ` `n = 7;` ` ` `cout << n << ` `"th centered nonadecagonal number : "` ` ` `<< center_nonadecagon_num(n);` ` ` `return` `0;` `}` |

## Java

`// Java Program to find nth centered` `// nonadecagonal number` `import` `java.io.*;` `class` `GFG {` ` ` ` ` `// centered nonadecagonal` ` ` `// function` ` ` `static` `int` `center_nonadecagon_num(` `int` `n)` ` ` `{` ` ` `// Formula to calculate nth` ` ` `// centered nonadecagonal number` ` ` `return` `(` `19` `* n * n - ` `19` `* n + ` `2` `) / ` `2` `;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `int` `n = ` `2` `;` ` ` `System.out.print ( n + ` `"th centered "` ` ` `+ ` `"nonadecagonal number : "` `);` ` ` `System.out.println (` ` ` `center_nonadecagon_num(n));` ` ` ` ` `n = ` `7` `;` ` ` `System.out.print ( n + ` `"th centered "` ` ` `+ ` `"nonadecagonal number : "` `);` ` ` `System.out.println(` ` ` `center_nonadecagon_num(n));` ` ` `}` `}` `// This code is contributed by m_kit` |

## Python3

`# Program to find nth` `# centered nonadecagonal number` `def` `center_nonadecagon_num(n) :` ` ` ` ` `# Formula to calculate` ` ` `# nth centered nonadecagonal` ` ` `# number & return it into` ` ` `# main function.` ` ` ` ` `return` `(` `19` `*` `n ` `*` `n ` `-` ` ` `19` `*` `n ` `+` `2` `) ` `/` `/` `2` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` `n ` `=` `2` ` ` `print` `(n,` `"nd centered nonadecagonal "` `+` ` ` `"number : "` `,` ` ` `center_nonadecagon_num(n))` ` ` `n ` `=` `7` ` ` `print` `(n,` `"nd centered nonadecagonal "` `+` ` ` `"number : "` `,` ` ` `center_nonadecagon_num(n))` `# This code is contributed by ajit` |

## C#

`// C# Program to find` `// nth centered` `// nonadecagonal number` `using` `System;` `class` `GFG` `{` ` ` ` ` `// centered nonadecagonal` ` ` `// function` ` ` `static` `int` `center_nonadecagon_num(` `int` `n)` ` ` `{` ` ` `// Formula to calculate nth` ` ` `// centered nonadecagonal number` ` ` `return` `(19 * n * n -` ` ` `19 * n + 2) / 2;` ` ` `}` ` ` ` ` `// Driver code` ` ` `static` `public` `void` `Main ()` ` ` `{` ` ` ` ` `int` `n = 2;` ` ` `Console.Write ( n + ` `"th centered "` `+` ` ` `"nonadecagonal number : "` `);` ` ` `Console.WriteLine(` ` ` `center_nonadecagon_num(n));` ` ` ` ` `n = 7;` ` ` `Console.Write( n + ` `"th centered "` `+` ` ` `"nonadecagonal number : "` `);` ` ` `Console.WriteLine(` ` ` `center_nonadecagon_num(n));` ` ` `}` `}` `// This code is contributed by ajit` |

## PHP

`<?php` `// PHP Program to find` `// nth centered` `// nonadecagonal number` `// centered nonadecagonal` `// function` `function` `center_nonadecagon_num( ` `$n` `)` `{` ` ` `// Formula to calculate nth` ` ` `// centered nonadecagonal number` ` ` `return` `(19 * ` `$n` `* ` `$n` `-` ` ` `19 * ` `$n` `+ 2) / 2;` `}` `// Driver Code` `$n` `= 2;` `echo` `$n` `,` `"th centered "` `+` ` ` `"nonadecagonal number : "` `,` ` ` `center_nonadecagon_num(` `$n` `);` `echo` `"\n"` `;` `$n` `= 7;` `echo` `$n` `, ` `"th centered "` `+` ` ` `"nonadecagonal number : "` `,` ` ` `center_nonadecagon_num(` `$n` `);` ` ` `// This code is contributed by ajit` `?>` |

## Javascript

`<script>` `// Javascript program to find nth centered` `// nonadecagonal number` `// centered nonadecagonal` `// function` `function` `center_nonadecagon_num(n)` `{` ` ` ` ` `// Formula to calculate nth` ` ` `// centered nonadecagonal number` ` ` `return` `(19 * n * n - 19 * n + 2) / 2;` `}` `// Driver Code` `var` `n = 2;` `document.write(n + ` `"th centered "` `+` ` ` `"nonadecagonal number : "` `);` `document.write(center_nonadecagon_num(n) + ` `"<br>"` `);` `n = 7;` `document.write(n + ` `"th centered "` `+` ` ` `"nonadecagonal number : "` `);` `document.write(center_nonadecagon_num(n));` `// This code is contributed by Kirti` ` ` `</script>` |

**Output :**

2th centered nonadecagonal number : 20 7th centered nonadecagonal numbe : 400

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

**References:**

http://oeis.org/A069132

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