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Count of 0s in an N-level hexagon
• Last Updated : 21 Oct, 2019

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

## 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, 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 `

Output:

```19
```

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