# Centered triangular number

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 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_Trigunal_num(n) << endl;` ` ` `// For 12th Centered Triangular number` ` ` `n = 12;` ` ` `cout << Centered_Triangular_num(n) << endl;` ` ` `return` `0;` `}` |

## 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

`<?php` `// PHP Program to find the` `//nth Centered Triangular number` `// function for Centered` `// Triangular number` `function` `Centered_Triangular_num(` `$n` `)` `{` ` ` `// formula for find Centered` ` ` `// Triangular number nth term` ` ` `return` `(3 * ` `$n` `* ` `$n` `+ 3 * ` `$n` `+ 2) / 2;` `}` `// Driver Code` ` ` `// For 3rd Centered Triangular number` ` ` `$n` `= 3;` ` ` `echo` `Centered_Triangular_num(` `$n` `), ` `"\n"` `;` ` ` `// For 12th Centered Triangular number` ` ` `$n` `= 12;` ` ` `echo` `Centered_Triangular_num(` `$n` `), ` `"\n"` `;` `// This code is contributed by aj_36` `?>` |

## Javascript

`<script>` `// javascript Program to find` `// the nth Centered` `// Triangular number` ` ` `// function for Centered` ` ` `// Triangular number` ` ` `function` `Centered_Triangular_num(n)` ` ` `{` ` ` ` ` `// formula for find Centered` ` ` `// Triangular number nth term` ` ` `return` `(3 * n * n + 3 * n + 2) / 2;` ` ` `}` ` ` `// Driver Code` ` ` ` ` `// For 3rd Centered` ` ` `// Triangular number` ` ` `var` `n = 3;` ` ` `document.write(Centered_Triangular_num(n)+` `"<br/>"` `);` ` ` `// For 12th Centered` ` ` `// Triangular number` ` ` `n = 12;` ` ` `document.write(Centered_Triangular_num(n)+` `"<br/>"` `);` `// This code is contributed by Rajput-Ji` `</script>` |

**Output :**

19 235

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

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