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Find the sum of the first N Centered Dodecagonal Number
  • Last Updated : 17 Mar, 2021

Given a number N, the task is to find the sum of first N Centered Dodecagonal Number.
 

The first few Centered Dodecagonal Numbers are 1, 13, 37, 73, 121, 181 … 
 

Examples: 
 

Input: N = 3 
Output: 51 
Explanation: 
1, 13 and 37 are the first three centered Dodecagonal number.
Input: N = 5 
Output: 245 
 

 



Approach: 
 

  1. Initially, create a function which will help us to calculate the Nth Centered Dodecagonal number.
  2. Run a loop starting from 1 to N, to find i-th Centered Dodecagonal number.
  3. Add all the above calculated Centered Dodecagonal numbers.
  4. Finally, display the sum of the first N Centered Dodecagonal numbers.

Below is the implementation of the above approach: 
 

C++




// C++ program to find the sum
// of the first N Centred
// Dodecagonal number
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the N-th 
// Centered Dodecagonal number
int Centered_Dodecagonal_num(int n)
{
     
    // Formula to calculate nth 
    // Centered_Dodecagonal number
    return 6 * n * (n - 1) + 1;
}
 
// Function to find the sum of the first
// N Centered_Dodecagonal number
int sum_Centered_Dodecagonal_num(int n)
{
     
    // Variable to store the sum
    int summ = 0;
     
    // Iterating from 1 to N
    for(int i = 1; i < n + 1; i++)
    {
 
       // Finding the sum
       summ += Centered_Dodecagonal_num(i);
    }
    return summ;
}
 
// Driver code
int main()
{
    int n = 5;
     
    cout << sum_Centered_Dodecagonal_num(n);
}
 
// This code is contributed by coder001

Java




// Java program to find the sum of the 
// first N centred dodecagonal number
class GFG {
     
// Function to find the N-th
// centered dodecagonal number
static int Centered_Dodecagonal_num(int n)
{
         
    // Formula to calculate nth
    // Centered_Dodecagonal number
    return 6 * n * (n - 1) + 1;
}
     
// Function to find the sum of the first
// N Centered_Dodecagonal number
static int sum_Centered_Dodecagonal_num(int n)
{
         
    // Variable to store the sum
    int summ = 0;
         
    // Iterating from 1 to N
    for(int i = 1; i < n + 1; i++)
    {
         
       // Finding the sum
       summ += Centered_Dodecagonal_num(i);
    }
    return summ;
}
     
// Driver code
public static void main (String[] args)
{
    int n = 5;
         
    System.out.print(sum_Centered_Dodecagonal_num(n));
}
}
 
// This code is contributed by AnkitRai01

Python3




# Python3 program to find the sum
# of the first N centred
# Dodecagonal number
 
# Function to find the
# N-th Centered Dodecagonal
# number
def Centered_Dodecagonal_num(n):
 
    # Formula to calculate 
    # nth Centered_Dodecagonal
    # number
    return 6 * n * (n - 1) + 1
     
   
# Function to find the
# sum of the first N
# Centered_Dodecagonal
# number
def sum_Centered_Dodecagonal_num(n) :
     
    # Variable to store the
    # sum
    summ = 0
     
    # Iterating from 1 to N
    for i in range(1, n + 1):
 
        # Finding the sum
        summ += Centered_Dodecagonal_num(i)
     
    return summ
   
# Driver code
if __name__ == '__main__' :
           
    n = 5
     
    print(sum_Centered_Dodecagonal_num(n))

C#




// C# program to find the sum of the
// first N centred dodecagonal number
using System;
 
class GFG{
     
// Function to find the N-th
// centered dodecagonal number
static int Centered_Dodecagonal_num(int n)
{
         
    // Formula to calculate nth
    // Centered_Dodecagonal number
    return 6 * n * (n - 1) + 1;
}
     
// Function to find the sum of the first
// N Centered_Dodecagonal number
static int sum_Centered_Dodecagonal_num(int n)
{
         
    // Variable to store the sum
    int summ = 0;
         
    // Iterating from 1 to N
    for(int i = 1; i < n + 1; i++)
    {
        
       // Finding the sum
       summ += Centered_Dodecagonal_num(i);
    }
    return summ;
}
     
// Driver code
public static void Main()
{
    int n = 5;
         
    Console.Write(sum_Centered_Dodecagonal_num(n));
}
}
 
// This code is contributed by Code_Mech

Javascript




<script>
 
    // Javascript program to find the sum 
    // of the first N Centred
    // Dodecagonal number
     
    // Function to find the N-th  
    // Centered Dodecagonal number 
    function Centered_Dodecagonal_num(n) 
    {
 
        // Formula to calculate nth  
        // Centered_Dodecagonal number
        return 6 * n * (n - 1) + 1;
    }
 
    // Function to find the sum of the first 
    // N Centered_Dodecagonal number
    function sum_Centered_Dodecagonal_num(n)
    {
 
        // Variable to store the sum
        let summ = 0;
 
        // Iterating from 1 to N
        for(let i = 1; i < n + 1; i++)
        {
 
           // Finding the sum
           summ += Centered_Dodecagonal_num(i);
        }
        return summ;
    }
     
    let n = 5;
       
    document.write(sum_Centered_Dodecagonal_num(n));
 
</script>
Output: 
245

 

Time Complexity: O(N).
 

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