Centered dodecahedral number
Given a number n, find then-th Centered Dodecahedral Number.
A Centered Dodecahedral number is class of figurative number.It is formed by a central dot, surrounded by successive dodecahedral(polyhedral with 12 flat surfaces) layers.
The first few Centered dodecahedral numbers (where n = 0, 1, 2, 3…….) are :
1, 33, 155, 427, 909, 1661 ……………
Examples:
Input : 5
Output : 1661
Input :1
Output :33
Mathematical formula for the nth Centered dodecahedral number is given by:
Below is the basic implementation of the above idea:
C++
#include <bits/stdc++.h>
using namespace std;
int CenteredDodecahedral_num( long int n)
{
return (2 * n + 1) * (5 * n * n + 5 * n + 1);
}
int main()
{
long int n = 3;
cout << n << "th Centered Dodecahedral number : " ;
cout << CenteredDodecahedral_num(n) << endl;
n = 10;
cout << n << "th Centered Dodecahedral number : " ;
cout << CenteredDodecahedral_num(n);
return 0;
}
|
C
#include <stdio.h>
int CenteredDodecahedral_num( long int n)
{
return (2 * n + 1) * (5 * n * n + 5 * n + 1);
}
int main()
{
long int n = 3;
printf ( "%ldth Centered Dodecahedral number : %d\n" ,n,CenteredDodecahedral_num(n));
n = 10;
printf ( "%ldth Centered Dodecahedral number : %d\n" ,n,CenteredDodecahedral_num(n));
return 0;
}
|
Java
import java.io.*;
class GFG {
static int CenteredDodecahedral_num( int n)
{
return ( 2 * n + 1 ) *
( 5 * n * n + 5 * n + 1 );
}
public static void main (String[] args)
{
int n = 3 ;
System.out.print( n + "th Centered "
+ "Dodecahedral number : " );
System.out.println (
CenteredDodecahedral_num(n));
n = 10 ;
System.out.print( n + "th Centered "
+ "Dodecahedral number : " );
System.out.println(
CenteredDodecahedral_num(n));
}
}
|
Python3
def CenteredDodecahedral_num(n) :
return ( 2 * n + 1 ) * ( 5 * n * n + 5 * n + 1 )
if __name__ = = '__main__' :
n = 3
print (n, "rd centered dodecahedral number: " ,
CenteredDodecahedral_num(n))
n = 10
print (n, "th centered dodecahedral number : " ,
CenteredDodecahedral_num(n))
|
C#
using System;
class GFG
{
static int CenteredDodecahedral_num( int n)
{
return (2 * n + 1) *
(5 * n * n +
5 * n + 1);
}
static public void Main ()
{
int n = 3;
Console.Write( n + "th Centered " +
"Dodecahedral number : " );
Console.WriteLine(
CenteredDodecahedral_num(n));
n = 10;
Console.Write( n + "th Centered " +
"Dodecahedral number : " );
Console.WriteLine(
CenteredDodecahedral_num(n));
}
}
|
PHP
<?php
function CenteredDodecahedral_num( $n )
{
return (2 * $n + 1) *
(5 * $n * $n +
5 * $n + 1);
}
$n = 3;
echo $n , "th Centered Dodecahedral " .
"number : " ;
echo CenteredDodecahedral_num( $n ), "\n" ;
$n = 10;
echo $n , "th Centered Dodecahedral " .
"number : " ;
echo CenteredDodecahedral_num( $n );
?>
|
Javascript
<script>
function CenteredDodecahedral_num(n)
{
return (2 * n + 1) *
(5 * n * n + 5 * n + 1);
}
var n = 3;
document.write(n + "th Centered " +
"Dodecahedral number : " );
document.write(CenteredDodecahedral_num(n) + "<br>" );
n = 10;
document.write(n + "th Centered " +
"Dodecahedral number : " );
document.write(CenteredDodecahedral_num(n));
</script>
|
Output :
3th Centered Dodecahedral number : 427
10th Centered Dodecahedral number : 11571
Time Complexity: O(1)
Auxiliary Space: O(1)
References:
https://en.wikipedia.org/wiki/Centered_dodecahedral_number
Last Updated :
20 May, 2022
Like Article
Save Article
Share your thoughts in the comments
Please Login to comment...