# Centered triangular number

• Difficulty Level : Basic
• Last Updated : 18 May, 2022

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++

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

## C

 `// C Program to find the``// nth Centered Triangular number``#include ` `// function for Centered``// Triangular number``int` `Centered_Triangular_num(``int` `n)``{``    ``// formula for find Centered``    ``// Triangular number nth term``    ``return` `(3 * n * n + 3 * n + 2) / 2;``}` `// Driver Code``int` `main()``{``    ``// For 3rd Centered Triangular number``    ``int` `n = 3;``    ``printf``(``"%d\n"``,Centered_Triangular_num(n));` `    ``// For 12th Centered Triangular number``    ``n = 12;``    ``printf``(``"%d\n"``,Centered_Triangular_num(n));` `    ``return` `0;``}` `// This code is contributed by kothavvsaakash.`

## Java

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

## Python3

 `# Program to find nth``# Centered Triangular number` `def` `Centered_Triangular_num(n) :``    ` `    ``# Formula to calculate nth``    ``# Centered Triangular number``    ``return` `(``3` `*` `n ``*` `n ``+``            ``3` `*` `n ``+` `2``) ``/``/` `2` `# Driver Code``if` `__name__ ``=``=` `'__main__'` `:` `    ``# For 3rd Centered``    ``# Triangular number    ``    ``n ``=` `3``    ``print``(Centered_Triangular_num(n))``    ` `    ``# For 12th Centered``    ``# Triangular number``    ``n ``=` `12``    ``print``(Centered_Triangular_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``// Triangular number``static` `int` `Centered_Triangular_num(``int` `n)``{``    ``// formula for find Centered``    ``// Triangular number nth term``    ``return` `(3 * n * n +``            ``3 * n + 2) / 2;``}` `// Driver Code``static` `public` `void` `Main ()``{` `// For 3rd Centered``// Triangular number``int` `n = 3;``Console.WriteLine(Centered_Triangular_num(n));` `// For 12th Centered``// Triangular number``n = 12;``Console.WriteLine(Centered_Triangular_num(n));``}``}` `// This code is contributed by akt_mit`

## PHP

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## Javascript

 ``

Output :

```19
235```

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

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