# Number of coloured 0’s in an N-level hexagon

Given an integer N, the task is to find the count of coloured 0s in an N-level hexagon when the 0s are coloured in the following way:

Examples:

Input: N = 2
Output: 5

Input: N = 3
Output: 12

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

Approach: For the values of N = 1, 2, 3, … it can be observed that a series will be formed as 1, 5, 12, 22, 35, …. It’s a difference series where differences are in AP as 4, 7, 10, 13, ….
Therefore the Nth term of will be 1 + {4 + 7 + 10 +13 +…..(n – 1) terms}
= 1 + (n – 1) * (2 * 4 + (n – 1 – 1) * 3) / 2
= 1 + (n – 1) * (8 + (n – 2) * 3) / 2
= 1 + (n – 1) * (8 + 3n – 6) / 2
= 1 + (n – 1) * (3n + 2) / 2
= n * (3 * n – 1) / 2

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the count of ` `// coloured 0s in an n-level hexagon ` `int` `count(``int` `n) ` `{ ` `    ``return` `n * (3 * n - 1) / 2; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 3; ` ` `  `    ``cout << count(n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `class` `GFG ` `{ ` `     `  `// Function to return the count of ` `// coloured 0s in an n-level hexagon ` `static` `int` `count(``int` `n) ` `{ ` `    ``return` `n * (``3` `* n - ``1``) / ``2``; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `n = ``3``; ` ` `  `    ``System.out.println(count(n)); ` `} ` `} ` ` `  `// This code is contributed by Code_Mech `

## Python3

 `# Python3 implementation of the approach  ` ` `  `# Function to return the count of  ` `# coloured 0s in an n-level hexagon  ` `def` `count(n) : ` ` `  `    ``return` `n ``*` `(``3` `*` `n ``-` `1``) ``/``/` `2``;  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `: ` ` `  `    ``n ``=` `3``;  ` ` `  `    ``print``(count(n));  ` ` `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# implementation of the approach  ` `using` `System; ` `     `  `class` `GFG ` `{ ` `     `  `// Function to return the count of ` `// coloured 0s in an n-level hexagon ` `static` `int` `count(``int` `n) ` `{ ` `    ``return` `n * (3 * n - 1) / 2; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `n = 3; ` ` `  `    ``Console.WriteLine(count(n)); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```12
```

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