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Centered triangular number
• Difficulty Level : Basic
• Last Updated : 31 Oct, 2018

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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

 ` `

Output :

```19
235
```

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