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Centered dodecahedral number

  • Last Updated : 20 Jul, 2021

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: 
 

Cd_{n}=(2n+1)(5n^2+5n+1)

Below is the basic implementation of the above idea:
 

C++




// Program to find nth centered
// dodecahedral number
#include <bits/stdc++.h>
using namespace std;
 
// Function to find
// centered dodecahedral number
int CenteredDodecahedral_num(long int n)
{
    // Formula to calculate nth
    // centered dodecahedral number
    // and return it into main function.
    return (2 * n + 1) * (5 * n * n + 5 * n + 1);
}
// Driver Code
int main()
{
    long int n = 3;
    // print result
    cout << n << "th Centered Dodecahedral number : ";
    cout << CenteredDodecahedral_num(n) << endl;
 
    n = 10;
    // print result
    cout << n << "th Centered Dodecahedral number : ";
    cout << CenteredDodecahedral_num(n);
 
    return 0;
}

Java




// Java Program to find nth
// centered dodecahedral number
import java.io.*;
 
class GFG {
 
    // Function to find centered
    // dodecahedral number
    static int CenteredDodecahedral_num(int n)
    {
         
        // Formula to calculate nth
        // centered dodecahedral number
        // and return it into main function.
         
        return (2 * n + 1) *
                     (5 * n * n + 5 * n + 1);
    }
     
    // Driver Code
    public static void main (String[] args)
    {
 
        int n = 3;
         
        // print result
        System.out.print( n + "th Centered "
                + "Dodecahedral number : ");
        System.out.println (
                CenteredDodecahedral_num(n));
 
        n = 10;
         
        // print result
        System.out.print( n + "th Centered "
                + "Dodecahedral number : ");
        System.out.println(
               CenteredDodecahedral_num(n));
    }
}
 
// This code is contributed by m_kit.

Python3




# Program to find nth centered
# dodecahedral number
 
# Function to find centered
# dodecahedral number
def CenteredDodecahedral_num(n) :
     
    # Formula to calculate nth
    # centered dodecahedral number
    return (2 * n + 1) * (5 * n * n + 5 * n + 1)
 
# Driver Code
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))
                 
# This code is contributed by aj_36

C#




// C# Program to find
// nth centered
// dodecahedral number
using System;
 
class GFG
{
     
    // Function to find
    // nth centered
    // dodecahedral number
    static int CenteredDodecahedral_num(int n)
    {
         
        // Formula to calculate
        // nth centered dodecahedral
        // number and return it
        // into main function.
        return (2 * n + 1) *
               (5 * n * n +
                5 * n + 1);
    }
     
    // Driver Code
    static public void Main ()
    {
        int n = 3;
         
        // print result
        Console.Write( n + "th Centered " +
                 "Dodecahedral number : ");
        Console.WriteLine(
                CenteredDodecahedral_num(n));
 
        n = 10;
         
        // print result
        Console.Write( n + "th Centered " +
                 "Dodecahedral number : ");
        Console.WriteLine(
                CenteredDodecahedral_num(n));
    }
}
 
// This code is contributed by ajit

PHP




<?php
// Program to find nth centered
// dodecahedral number
 
// Function to find
// centered dodecahedral number
function CenteredDodecahedral_num($n)
{
    // Formula to calculate nth
    // centered dodecahedral number
    // and return it into main function.
    return (2 * $n + 1) *
           (5 * $n * $n +
            5 * $n + 1);
}
 
// Driver Code
$n = 3;
// print result
echo $n, "th Centered Dodecahedral " .
                          "number : ";
echo CenteredDodecahedral_num($n),"\n";
 
$n = 10;
// print result
echo $n, "th Centered Dodecahedral " .
                          "number : ";
echo CenteredDodecahedral_num($n);
 
// This code is contributed by akt_mit
?>

Javascript




<script>
 
// Javascript Program to find nth
// centered dodecahedral number
 
// Function to find centered
// dodecahedral number
function CenteredDodecahedral_num(n)
{
     
    // Formula to calculate nth
    // centered dodecahedral number
    // and return it into main function.
    return (2 * n + 1) *
           (5 * n * n + 5 * n + 1);
}
     
// Driver code
var n = 3;
         
// print result
document.write(n + "th Centered " +
               "Dodecahedral number : ");
document.write(CenteredDodecahedral_num(n) + "<br>");
 
n = 10;
 
// print result
document.write(n + "th Centered " +
               "Dodecahedral number : ");
document.write(CenteredDodecahedral_num(n));
 
// This code is contributed by Khushboogoyal499
 
</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
 

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