Find the sum of the first N Centered Dodecagonal Number

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 N^th 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 Centered
// 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 centered 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 centered
# 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 centered 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 Centered
    // 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).

Auxiliary Space: O(1) since constant variables are being used