Centered Hexadecagonal Number
Given a number n, find the nth Centered Hexadecagonal Number.
A Centered Hexadecagonal number represents a dot in the center and other dots around it in successive hexadecagonal(16 sided polygon) layers.
The first few Centered Hexadecagonal numbers are:
1, 17, 49, 97, 161, 241, 337, 449, 577, 721, 881………………….
Examples :
Input : 3
Output : 49
Input : 10
Output : 721
In mathematics, Centered hexadecagonal number for the n-th term is given by :
Below is the basic implementation of the above idea:
C++
#include <bits/stdc++.h>
using namespace std;
int center_hexadecagonal_num( long int n)
{
return 8 * n * n - 8 * n + 1;
}
int main()
{
long int n = 2;
cout << n << "th centered hexadecagonal number : "
<< center_hexadecagonal_num(n);
cout << endl;
n = 12;
cout << n << "th centered hexadecagonal number : "
<< center_hexadecagonal_num(n);
return 0;
}
|
C
#include <stdio.h>
int center_hexadecagonal_num( long int n)
{
return 8 * n * n - 8 * n + 1;
}
int main()
{
long int n = 2;
printf ( "%ldth centered hexadecagonal number : %d\n" ,n,center_hexadecagonal_num(n));
n = 12;
printf ( "%ldth centered hexadecagonal number : %d\n" ,n,center_hexadecagonal_num(n));
return 0;
}
|
Java
import java.io.*;
class GFG
{
static int center_hexadecagonal_num( int n)
{
return 8 * n * n -
8 * n + 1 ;
}
public static void main(String args[])
{
int n = 2 ;
System.out.print(n + "th centered " +
"hexadecagonal number: " );
System.out.println(center_hexadecagonal_num(n));
n = 12 ;
System.out.print(n + "th centered " +
"hexadecagonal number: " );
System.out.println(center_hexadecagonal_num(n));
}
}
|
Python3
def center_hexadecagonal_num(n):
return 8 * n * n - 8 * n + 1
if __name__ = = '__main__' :
n = 2
print (n, "nd centered hexadecagonal " +
"number : " ,
center_hexadecagonal_num(n))
n = 12
print (n, "th centered hexadecagonal " +
"number : " ,
center_hexadecagonal_num(n))
|
C#
using System;
class GFG
{
static int center_hexadecagonal_num( int n)
{
return 8 * n * n -
8 * n + 1;
}
static public void Main ()
{
int n = 2;
Console.Write(n + "th centered " +
"hexadecagonal number: " );
Console.WriteLine(center_hexadecagonal_num(n));
n = 12;
Console.Write(n + "th centered " +
"hexadecagonal number: " );
Console.WriteLine(center_hexadecagonal_num(n));
}
}
|
PHP
<?php
function center_hexadecagonal_num( $n )
{
return 8 * $n * $n - 8 * $n + 1;
}
$n = 2;
echo $n , "th centered hexadecagonal number : " ,
center_hexadecagonal_num( $n );
echo "\n" ;
$n = 12;
echo $n , "th centered hexadecagonal numbe : " ,
center_hexadecagonal_num( $n );
?>
|
Javascript
<script>
function center_hexadecagonal_num(n)
{
return 8 * n * n - 8 * n + 1;
}
var n = 2;
document.write(n + "th centered " +
"hexadecagonal number: " );
document.write(center_hexadecagonal_num(n) + "<br>" );
n = 12;
document.write(n + "th centered " +
"hexadecagonal number: " );
document.write(center_hexadecagonal_num(n));
</script>
|
Output :
2nd centered hexadecagonal number : 17
12th centered hexadecagonal number : 1057
Time Complexity: O(1)
Auxiliary Space: O(1)
References:
http://oeis.org/A069129
Last Updated :
31 Mar, 2023
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