Centered hexagonal number

Given a number n and the task is to find n^th centered hexagonal number. Also find the Centered hexagonal series.
A centered hexagonal number or hex number is centered figure number that represents a hexagon with dot in center and all other dot surrounding in hexagonal form. N^th centered hexagonal number can be calculated by using formula 3n(n – 1) + 1.

Examples :

Input : n = 2
Output : 7

Input : n = 10
Output : 271

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

C++

// Program to find nth  
// centered hexadecimal number. 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to find centered 
// hexadecimal number. 
int centeredHexagonalNumber(int n) 
{ 
    // Formula to calculate nth  
    // centered hexadecimal number  
    // and return it into main function. 
    return 3 * n * (n - 1) + 1; 
} 
  
// Driver Code 
int main() 
{ 
    int n = 10; 
    cout << n << "th centered hexagonal number: "; 
    cout << centeredHexagonalNumber(n); 
    return 0; 
} 

Java

// Java Program to find nth 
// centered hexadecimal number 
import java.io.*; 
  
class GFG  
{ 
      
    // Function to find centered 
    // hexadecimal number 
    static int centeredHexagonalNumber(int n) 
    { 
        // Formula to calculate nth  
        // centered hexadecimal number 
        // and return it into main function 
        return 3 * n * (n - 1) + 1; 
    } 
      
    // Driver Code 
    public static void main(String args[]) 
    { 
        int n = 10; 
        System.out.print(n + "th centered " + 
                       "hexagonal number: "); 
        System.out.println(centeredHexagonalNumber(n)); 
          
    } 
} 
  
// This code is contributed by Nikita Tiwari. 

Python3

# Python 3 program to find nth  
# centered hexagonal number 
  
# Function to find  
# centered hexagonal number 
def centeredHexagonalNumber(n) : 
      
    # Formula to calculate  
    # nth centered hexagonal 
    return 3 * n * (n - 1) + 1
  
  
# Driver Code 
if __name__ == '__main__' : 
          
    n = 10
    print(n, "th centered hexagonal number: "
                , centeredHexagonalNumber(n)) 
  
  
# This code is contributed 
# by 'Akanshgupta' 

C#

// C# Program to find nth  
// centered hexadecimal number 
using System; 
  
class GFG 
{ 
      
    // Function to find centered  
    // hexadecimal number 
    static int centeredHexagonalNumber(int n) 
    { 
        // Formula to calculate nth  
        // centered hexadecimal number  
        // and return it into main function 
        return 3 * n * (n - 1) + 1; 
    } 
      
    // Driver Code 
    public static void Main() 
    { 
        int n = 10; 
        Console.Write(n + "th centered "+  
                   "hexagonal number: "); 
        Console.Write(centeredHexagonalNumber(n)); 
          
    } 
} 
  
// This code is contributed by vt_m. 

PHP

<?php 
// PHP Program to find nth  
// centered hexadecimal number. 
  
// Function to find centered 
// hexadecimal number. 
function centeredHexagonalNumber( $n) 
{ 
      
    // Formula to calculate nth 
    // centered hexadecimal 
    // number and return it  
    // into main function. 
    return 3 * $n * ($n - 1) + 1; 
} 
  
    // Driver Code 
    $n = 10; 
    echo $n , "th centered hexagonal number: "; 
    echo centeredHexagonalNumber($n); 
  
// This code is contributed by anuj_67. 
?> 

Output :

10th centered hexagonal number: 271

Time Complexity : O(1)

Given a number n and the task is to find centered hexagonal series till n.
We can also find centered hexagonal series.

C++

// Program to find the series  
// of centered hexadecimal number 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to find the  
// series of centered  
// hexadecimal number. 
void centeredHexagonalSeries(int n) 
{ 
    // Formula to calculate  
    // nth centered hexadecimal 
    // number. 
    for (int i = 1; i <= n; i++) 
        cout << 3 * i * (i - 1) + 1  
             << " "; 
} 
  
// Driver Code 
int main() 
{ 
    int n = 10; 
    centeredHexagonalSeries(n); 
    return 0; 
} 

Java

// Program to find the series of  
// centered hexadecimal number. 
import java.io.*; 
  
class GFG  
{ 
    // Function to find the series of  
    // centered hexadecimal number. 
    static void centeredHexagonalSeries(int n) 
    { 
        // Formula to calculate nth  
        // centered hexadecimal number. 
        for (int i = 1; i <= n; i++) 
            System.out.print( 3 * i *  
                            (i - 1) + 1 + " "); 
    } 
      
    // Driver Code 
    public static void main(String args[]) 
    { 
        int n = 10; 
        centeredHexagonalSeries(n); 
    } 
} 
  
// This code is contributed by Nikita Tiwari. 

Python3

# Python3 program to find  
# nth centered hexagonal number 
  
# Function to find centered hexagonal  
# series till n given numbers. 
def centeredHexagonalSeries(n) : 
    for i in range(1, n + 1) : 
          
        # Formula to calculate nth 
        # centered hexagonal series. 
        print(3 * i * (i - 1) + 1, end=" ") 
          
# Driver Code 
if __name__ == '__main__' : 
      
    n = 10
    centeredHexagonalSeries(n) 
  
# This code is contributed  
# by 'Akanshgupta' 

C#

// C# Program to find the  
// series of centered  
// hexadecimal number. 
using System; 
  
class GFG  
{ 
      
    // Function to find the  
    // series of centered  
    // hexadecimal number. 
    static void centeredHexagonalSeries(int n) 
    { 
        // Formula to calculate nth  
        // centered hexadecimal number. 
        for (int i = 1; i <= n; i++) 
            Console.Write( 3 * i *  
                         (i - 1) + 1 + " "); 
    } 
      
    // Driver Code 
    public static void Main() 
    { 
        int n = 10; 
        centeredHexagonalSeries(n); 
    } 
} 
  
// This code is contributed by vt_m. 

PHP

<?php 
// Program to find the  
// series of centered  
// hexadecimal number. 
  
// Function to find the  
// series of centered  
// hexadecimal number. 
function centeredHexagonalSeries( $n) 
{ 
    // Formula to calculate 
    // nth centered hexadecimal  
    // number. 
    for ( $i = 1; $i <= $n; $i++) 
    echo 3 * $i * ($i - 1) + 1 ," "; 
} 
  
// Driver Code 
$n = 10; 
centeredHexagonalSeries($n); 
  
// This code is contributed by anuj_67. 
?> 

Output :

1 7 19 37 61 91 127 169 217 271

My Personal Notes

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

C++

Java

Python3

C#

PHP

C++

Java

Python3

C#

PHP

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