Find the sum of the first N Dodecagonal Numbers

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

The first few dodecagonal numbers are 1, 12, 33, 64, 105, 156, 217 …

Examples:

Input: N = 3 
Output: 46 
Explanation:
1, 12 and 33 are the first three Dodecagonal numbers

Input: N = 5 
Output: 215 

Approach:

1. Initially, we need to create a function that will help us to calculate the N^th Dodecagonal number.
2. Run a loop starting from 1 to N, to find ith Dodecagonal number.
3. Add all the above calculated Dodecagonal numbers.
4. Finally, display the sum of the first N Dodecagonal numbers.

Below is the implementation of the above approach: 

C++

// C++ program to find the sum of
// the first N dodecagonal numbers
#include <bits/stdc++.h>
using namespace std;

// Function to find the N-th
// dodecagonal number
int Dodecagonal_num(int n)
{

    // Formula to calculate N-th
    // dodecagonal number
    return (5 * n * n - 4 * n);
}

// Function to find the sum of
// the first N dodecagonal numbers
int sum_Dodecagonal_num(int n)
{

    // Variable to get the sum
    int summ = 0;

    // Iterating through the
    // first N numbers
    for(int i = 1; i < n + 1; i++)
    {

        // Compute the sum
        summ += Dodecagonal_num(i);
    }
    return summ;
}

// Driver Code
int main()
{
    int n = 5;

    // Display first Nth
    // centered_decagonal number
    cout << (sum_Dodecagonal_num(n));
    return 0;
}

// This code is contributed by PrinciRaj1992

Java

// Java program to find the sum of
// the first N dodecagonal numbers
class GFG {

// Function to find the N-th
// dodecagonal number
static int Dodecagonal_num(int n)
{

    // Formula to calculate N-th
    // dodecagonal number
    return (5 * n * n - 4 * n);
}

// Function to find the sum of
// the first N dodecagonal numbers
static int sum_Dodecagonal_num(int n)
{

    // Variable to get the sum
    int summ = 0;

    // Iterating through the
    // first N numbers
    for(int i = 1; i < n + 1; i++)
    {

       // Compute the sum
       summ += Dodecagonal_num(i);
    }
    return summ;
}

// Driver Code
public static void main(String[] args)
{
    int n = 5;

    // Display first Nth
    // centered_decagonal number
    System.out.println(sum_Dodecagonal_num(n));
}
}

// This code is contributed by sapnasingh4991

Python3

# Python3 program to find the
# sum of the first N
# Dodecagonal numbers

# Function to find the N-th
# Dodecagonal number
def Dodecagonal_num(n):

    # Formula to calculate
    # N-th Dodecagonal
    # number
    return (5 * n * n - 4 * n)


# Function to find the
# sum of the first N
# Dodecagonal numbers
def sum_Dodecagonal_num(n) :

    # Variable to get the sum
    summ = 0

    # Iterating through the
    # first N numbers
    for i in range(1, n + 1):

        # Compute the sum
        summ += Dodecagonal_num(i)

    return summ

# Driver Code
if __name__ == '__main__' :

    n = 5

    print(sum_Dodecagonal_num(n))

C#

// C# program to find the sum of
// the first N dodecagonal numbers
using System;

class GFG {

// Function to find the N-th
// dodecagonal number
static int Dodecagonal_num(int n)
{

    // Formula to calculate N-th
    // dodecagonal number
    return (5 * n * n - 4 * n);
}

// Function to find the sum of
// the first N dodecagonal numbers
static int sum_Dodecagonal_num(int n)
{

    // Variable to get the sum
    int summ = 0;

    // Iterating through the
    // first N numbers
    for(int i = 1; i < n + 1; i++)
    {

        // Compute the sum
        summ += Dodecagonal_num(i);
    }
    return summ;
}

// Driver Code
public static void Main(String[] args)
{
    int n = 5;

    // Display first Nth
    // centered_decagonal number
    Console.WriteLine(sum_Dodecagonal_num(n));
}
}

// This code is contributed by sapnasingh4991

Javascript

<script>

    // Javascript program to find the sum of
    // the first N dodecagonal numbers

    // Function to find the N-th
    // dodecagonal number
    function Dodecagonal_num(n)
    {

        // Formula to calculate N-th
        // dodecagonal number
        return (5 * n * n - 4 * n);
    }

    // Function to find the sum of
    // the first N dodecagonal numbers
    function sum_Dodecagonal_num(n)
    {

        // Variable to get the sum
        let summ = 0;

        // Iterating through the
        // first N numbers
        for(let i = 1; i < n + 1; i++)
        {

            // Compute the sum
            summ += Dodecagonal_num(i);
        }
        return summ;
    }

    let n = 5;

    // Display first Nth
    // centered_decagonal number
    document.write(sum_Dodecagonal_num(n));

</script>

Output

215

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