Centered hexagonal number (original) (raw)

Last Updated : 13 Jul, 2021

Given a number N and the task is to find Nth centered hexagonal number. Also, find the Centered hexagonal series.
Examples:

Input: N = 2
Output: 7
Input: N = 10
Output: 271

Centered Hexagonal Numbers - The Centered Hexagonal numbers are figurate numbers and are in the form of the Hexagon. The Centered Hexagonal number is different from Hexagonal Number because it contains one element at the center.
Some of the Central Hexagonal numbers are -

1, 7, 19, 37, 61, 91, 127, 169 ...

For Example:

The First N numbers are - 1, 7, 19, 37, 61, 91, 127 ...

The cumulative sum of these numbers are - 1, 1+7, 1+7+19, 1+7+19+37...

which is nothing but the sequence - 1, 8, 27, 64, 125, 216 ...

That is in the form of - 13, 23, 33, 43, 53, 63 ....

As Central Hexagonal numbers sum up to Nth term will be the N3. That is -

13 + 23 + 33 + 43 + 53 + 63 .... upto N terms = N3
Then, Nth term will be -
=> N3 - (N - 1)3
=> 3*N*(N - 1) + 1

Approach: For finding the Nth term of the Centered Hexagonal Number use the formulae - 3*N*(N - 1) + 1.
Below is the implementation of the above approach:

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

JavaScript

`

Output :

10th centered hexagonal number: 271

Performance Analysis:

• Time Complexity: In the above given approach we are finding the Nth term of the Centered Hexagonal Number which takes constant time. Therefore, the complexity will be O(1)
• Space Complexity: In the above given approach, we are not using any other auxiliary space for the computation. Therefore, the space complexity will be O(1).

Centered Hexagonal series

Given a number N, the task is to find centered hexagonal series till N.
Approach:
Iterate the loop using a loop variable (say i) and find the each ith term of the Centered Hexagonal Number using the formulae - 3*i*(i - 1) + 1
Below is the implementation of the above approach:

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

JavaScript

`

Output :

1 7 19 37 61 91 127 169 217 271

Time Complexity: O(n)
Auxiliary Space: O(1)