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Centered triangular number
• Difficulty Level : Basic
• Last Updated : 26 Mar, 2021

Given an integer n, find the nth Centered triangular number.
Centered Triangular Number is a centered polygonal number that represents a triangle with a dot in the centre and all other dots surrounding the centre in successive triangular layers [Source : Wiki ]
Pictorial Representation : The first few centered triangular number series are :
1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, 199, 235, 274, 316, 361, 409, 460………………………..
Examples:

```Input : n = 1
Output : 4
Explanation :
A dot in the centre and 3 dots forming the
triangle outside it, thus 4.

Input : n = 6
Output : 64

Input : n = 10
Output : 166```

Approach
nth Term of centered triangular number is given by:

` `

Basic Implementation of the above approach:

## C++

 `// CPP Program to find the``// nth Centered Trigunal number``#include``using` `namespace` `std;` `// function for Centered``// Trigunal number``int` `Centered_Trigunal_num(``int` `n)``{``    ``// formula for find Centered``    ``// Trigunal number nth term``    ``return` `(3 * n * n + 3 * n + 2) / 2;``}` `// Driver Code``int` `main()``{``    ``// For 3rd Centered Trigunal number``    ``int` `n = 3;``    ``cout << Centered_Trigunal_num(n) << endl;` `    ``// For 12th Centered Trigunal number``    ``n = 12;``    ``cout << Centered_Trigunal_num(n) << endl;` `    ``return` `0;``}`

## Java

 `// Java Program to find``// the nth Centered``// Triangular number``import` `java.io.*;` `class` `GFG``{``    ` `// function for Centered``// Trigunal number``static` `int` `Centered_Trigunal_num(``int` `n)``{``    ``// formula for find Centered``    ``// Trigunal number nth term``    ``return` `(``3` `* n * n +``            ``3` `* n + ``2``) / ``2``;``}` `// Driver Code``public` `static` `void` `main (String[] args)``{` `// For 3rd Centered``// Trigunal number``int` `n = ``3``;``System.out.println(Centered_Trigunal_num(n));` `// For 12th Centered``// Trigunal number``n = ``12``;``System.out.println(Centered_Trigunal_num(n));``}``}` `// This code is contributed by ajit`

## Python3

 `# Program to find nth``# Centered Trigunal number` `def` `Centered_Trigunal_num(n) :``    ` `    ``# Formula to calculate nth``    ``# Centered Trigunal number``    ``return` `(``3` `*` `n ``*` `n ``+``            ``3` `*` `n ``+` `2``) ``/``/` `2` `# Driver Code``if` `__name__ ``=``=` `'__main__'` `:` `    ``# For 3rd Centered``    ``# Trigunal number    ``    ``n ``=` `3``    ``print``(Centered_Trigunal_num(n))``    ` `    ``# For 12th Centered``    ``# Trigunal number``    ``n ``=` `12``    ``print``(Centered_Trigunal_num(n))``                ` `                ` `# This code is contributed``# by akt_mit`

## C#

 `// C# Program to find``// the nth Centered``// Triangular number``using` `System;` `class` `GFG``{` `// function for Centered``// Trigunal number``static` `int` `Centered_Trigunal_num(``int` `n)``{``    ``// formula for find Centered``    ``// Trigunal number nth term``    ``return` `(3 * n * n +``            ``3 * n + 2) / 2;``}` `// Driver Code``static` `public` `void` `Main ()``{` `// For 3rd Centered``// Trigunal number``int` `n = 3;``Console.WriteLine(Centered_Trigunal_num(n));` `// For 12th Centered``// Trigunal number``n = 12;``Console.WriteLine(Centered_Trigunal_num(n));``}``}` `// This code is contributed by akt_mit`

## PHP

 ``

## Javascript

 ``

Output :

```19
235```

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