# Count of 0s in an N-level hexagon

Given an integer N, the task is to find the count of 0s in an N-level hexagon.

Examples:

Input: N = 2
Output: 7
Input: N = 3
Output: 19

Approach: For the values of N = 1, 2, 3, … it can be observed that a series will be formed as 1, 7, 19, 37, 61, 91, 127, 169, …. It’s a difference series where differences are in AP as 6, 12, 18, …
Therefore the Nth term of will be 1 + {6 + 12 + 18 +…..(n – 1) terms}
= 1 + (n – 1) * (2 * 6 + (n – 1 – 1) * 6) / 2
= 1 + (n – 1) * (12 + (n – 2) * 6) / 2
= 1 + (n – 1) * (12 + 6n – 12) / 2
= 1 + (n – 1) * (6n) / 2
= 1 + (n – 1) * (3n)
Below is the implementation of the above approach:

## C++

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

## Java

 `// Java implementation of the above approach ``class` `GFG ``{``    ` `    ``// Function to return the count of ``    ``// 0s in an n-level hexagon ``    ``static` `int` `count(``int` `n) ``    ``{ ``        ``return` `3` `* n * (n - ``1``) + ``1``; ``    ``} ``    ` `    ``// Driver code ``    ``public` `static` `void` `main(String args[]) ``    ``{ ``        ``int` `n = ``3``; ``    ` `        ``System.out.println(count(n)); ``    ``} ``}` `// This code is contributed by AnkitRai01`

## Python3

 `# Python3 implementation of the approach` `# Function to return the count of``# 0s in an n-level hexagon``def` `count(n):``    ``return` `3` `*` `n ``*` `(n ``-` `1``) ``+` `1` `# Driver code``n ``=` `3` `print``(count(n))` `# This code is contributed by Mohit Kumar`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{``    ` `// Function to return the count of``// 0s in an n-level hexagon``static` `int` `count(``int` `n)``{``    ``return` `3 * n * (n - 1) + 1;``}` `// Driver code``static` `public` `void` `Main ()``{``    ``int` `n = 3;``    ` `    ``Console.Write(count(n));``}``}` `// This code is contributed by ajit`

## Javascript

 ``

Output:
`19`

Time Complexity: O(1)

Auxiliary Space: O(1)

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