Last Updated : 13 Jul, 2021
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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
<?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.
?>
Javascript
<script>
// 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
let n = 10;
document.write(n +
"th centered hexagonal number: "
);
document.write(centeredHexagonalNumber(n));
// This code is contributed by rishavmahato348.
</script>
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
<?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.
?>
Javascript
<script>
// JavaScript 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
(let i = 1; i <= n; i++)
document.write( 3 * i *
(i - 1) + 1 +
" "
);
}
// Driver code
let n = 10;
centeredHexagonalSeries(n);
</script>
Output :
1 7 19 37 61 91 127 169 217 271
Time Complexity: O(n)
Auxiliary Space: O(1)
Dharmendra_Kumar
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