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

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++

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// C++ implementation of the approach
#include <bits/stdc++.h>
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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output:

12

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