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:

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

Below is the basic implementation of the above idea:

C++

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// 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;
}

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Java

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// 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.

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Python3

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# 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

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C#

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// 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

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PHP

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<?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
?>

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Output :

3th Centered Dodecahedral number : 427
10th Centered Dodecahedral number : 11571

References:
https://en.wikipedia.org/wiki/Centered_dodecahedral_number



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