Centered Dodecagonal Number

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++

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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output :

13
433

References
http://oeis.org/A003154

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