Skip to content
Related Articles

# Centered nonadecagonal number

• Last Updated : 20 Jul, 2021

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 ``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

 ``

## Javascript

 ``

Output :

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

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

References:
http://oeis.org/A069132

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.

My Personal Notes arrow_drop_up