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Centered Dodecagonal Number

  • Last Updated : 13 Jul, 2021

Given a number n, find the nth Centered Dodecagonal Number. 
The Centered Dodecagonal Number represents a dot in the center and other dots surrounding it in successive dodecagonal(12 sided polygon) layers. 
Examples : 
 

Input :  3
Output : 37

Input : 7
Output :253 

 

centered dodecagonal number

The first few centered dodecagonal numbers are: 
1, 13, 37, 73, 121, 181, 253, 337, 433, 541, 661…………………..
The formula for the nth Centered dodecagonal number:
 

CDg_{n}= 6n(n-1)+1

 



C++




// C++ Program to find
// nth centered
// Dodecagonal number
#include <bits/stdc++.h>
using namespace std;
 
// Function to calculate Centered
// Dodecagonal number
int centeredDodecagonal(long int n)
{
    // Formula to calculate nth
    // centered Dodecagonal number
    return 6 * n * (n - 1) + 1;
}
 
// Driver Code
int main()
{
    long int n = 2;
    cout << centeredDodecagonal(n);
    cout << endl;
    n = 9;
    cout << centeredDodecagonal(n);
 
    return 0;
}

Java




// Java Program to find nth
// centered dodecagonal number
import java.io.*;
 
class GFG{
     
// Function to calculate
// centered dodecagonal number
static long centeredDodecagonal(long n)
{
     
    // Formula to calculate nth
    // centered dodecagonal number
    return 6 * n * (n - 1) + 1;
}
 
// Driver Code
public static void main(String[] args)
{
    long n = 2;
    System.out.println(centeredDodecagonal(n));
 
    n = 9;
    System.out.println(centeredDodecagonal(n));
}
}
 
// This code is contributed by anuj_67

Python3




# Python3 program to find nth
# centered dodecagonal number
 
# Function to calculate
# centered dodecagonal number
def centeredDodecagonal(n) :
     
    # Formula to calculate nth
    # centered dodecagonal number
    return 6 * n * (n - 1) + 1;
 
# Driver code
n = 2
print(centeredDodecagonal(n));
 
n = 9
print(centeredDodecagonal(n));
 
# This code is contributed by grand_master

C#




// C# Program to find nth
// centered dodecagonal number
using System;
class GFG{
 
// Function to calculate
// centered dodecagonal number
static long centeredDodecagonal(long n)
{
     
    // Formula to calculate nth
    // centered dodecagonal number
    return 6 * n * (n - 1) + 1;
}
 
// Driver Code
public static void Main(String[] args)
{
    long n = 2;
    Console.WriteLine(centeredDodecagonal(n));
     
    n = 9;
    Console.WriteLine(centeredDodecagonal(n));
}
}
 
// This code is contributed by shivanisinghss2110

Javascript




<script>
 
// Javascript Program to find
// nth centered
// Dodecagonal number
 
// Function to calculate Centered
// Dodecagonal number
function centeredDodecagonal(n)
{
 
    // Formula to calculate nth
    // centered Dodecagonal number
    return 6 * n * (n - 1) + 1;
}
 
// Driver Code
let n = 2;
document.write(centeredDodecagonal(n));
document.write("<br>");
n = 9;
document.write(centeredDodecagonal(n));
 
// This code is contributed by rishavmahato348.
</script>
Output : 
13
433

 

Time Complexity: O(1)
Auxiliary Space: O(1)

References 
http://oeis.org/A003154
 

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