Find the sum of the first Nth Centered Tridecagonal Numbers

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

A Centered tridecagonal number represents a dot at the center and other dots surrounding the center dot in the successive tridecagonal(13 sided polygon) layer. The first few Centered tridecagonal numbers are 1, 14, 40, 79 … 

Examples:

Input: N = 3 
Output: 55 
Explanation:
1, 14 and 40 are the first three Centered tridecagonal number. 
1 + 14 + 40 = 55.

Input: N = 5 
Output: 265 

Approach:

1. Initially, we need to create a function which will help us to calculate the N^th Centered tridecagonal number.
2. Now, Run a loop starting from 1 to N, and find the Centered tridecagonal numbers in this range.
3. Add all the above calculated Centered tridecagonal numbers.
4. Finally, display the sum of the first N Centered tridecagonal numbers.

Below is the implementation of the above approach: 

C++

// C++ program to find the sum of
// the first Nth centered
// tridecagonal number
#include<bits/stdc++.h>
using namespace std;

// Function to calculate the
// N-th centered tridecagonal
// number
int Centered_tridecagonal_num(int n)
{
    // Formula to calculate
    // Nth centered tridecagonal
    // number & return it
    return (13 * n * (n - 1) + 2) / 2;
}

// Function to find the sum
// of the first N centered
// tridecagonal numbers
int sum_Centered_tridecagonal_num(int n)
{
    // Variable to store
    // the sum
    int summ = 0;

    // Loop to iterate and find the
    // sum of first N centered
    // tridecagonal numbers
    for(int i = 1; i <= n; i++)
    {
        summ += Centered_tridecagonal_num(i);
    }
    return summ ;
}

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

    cout << sum_Centered_tridecagonal_num(n)
         << endl;
    return 0;
}

// This code is contributed by rutvik_56

Java

// Java program to find the sum of
// the first Nth centered
// tridecagonal number
class GFG{

// Function to calculate the
// N-th centered tridecagonal
// number
public static int Centered_tridecagonal_num(int n)
{

    // Formula to calculate
    // Nth centered tridecagonal
    // number & return it
    return (13 * n * (n - 1) + 2) / 2;
}

// Function to find the sum
// of the first N centered
// tridecagonal numbers
public static int sum_Centered_tridecagonal_num(int n)
{

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

    // Loop to iterate and find the
    // sum of first N centered
    // tridecagonal numbers
    for(int i = 1; i <= n; i++)
    {
       summ += Centered_tridecagonal_num(i);
    }
    return summ ;
}

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

    System.out.println(sum_Centered_tridecagonal_num(n));
}
}

// This code is contributed by divyeshrabadiya07

Python3

# Program to find the sum of
# the first Nth
# Centered_tridecagonal number

# Function to calculate the
# N-th Centered tridecagonal
# number
def Centered_tridecagonal_num(n):

    # Formula to calculate
    # Nth Centered tridecagonal
    # number & return it
    return (13 * n *
           (n - 1) + 2) // 2


# Function to find the sum
# of the first N
# Centered tridecagonal
# numbers
def sum_Centered_tridecagonal_num(n) :

    # Variable to store
    # the sum
    summ = 0

    # Loop to iterate and find the
    # sum of first N Centered
    # tridecagonal numbers
    for i in range(1, n + 1):


        summ += Centered_tridecagonal_num(i)

    return summ

# Driver Code
if __name__ == '__main__' :

    n = 5

    print(sum_Centered_tridecagonal_num(n))

C#

// C# program to find the sum of
// the first Nth centered
// tridecagonal number
using System;

class GFG{

// Function to calculate the
// N-th centered tridecagonal
// number
public static int Centered_tridecagonal_num(int n)
{

    // Formula to calculate
    // Nth centered tridecagonal
    // number & return it
    return (13 * n * (n - 1) + 2) / 2;
}

// Function to find the sum
// of the first N centered
// tridecagonal numbers
public static int sum_Centered_tridecagonal_num(int n)
{

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

    // Loop to iterate and find the
    // sum of first N centered
    // tridecagonal numbers
    for(int i = 1; i <= n; i++)
    {
       summ += Centered_tridecagonal_num(i);
    }
    return summ;
}

// Driver code
public static void Main()
{
    int n = 5;

    Console.WriteLine(sum_Centered_tridecagonal_num(n));
}
}

// This code is contributed by Code_Mech

Javascript

<script>

    // Javascript program to find the sum of
    // the first Nth centered
    // tridecagonal number

    // Function to calculate the
    // N-th centered tridecagonal
    // number
    function Centered_tridecagonal_num(n)
    {

        // Formula to calculate
        // Nth centered tridecagonal
        // number & return it
        return (13 * n * (n - 1) + 2) / 2;
    }

    // Function to find the sum
    // of the first N centered
    // tridecagonal numbers
    function sum_Centered_tridecagonal_num(n)
    {

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

        // Loop to iterate and find the
        // sum of first N centered
        // tridecagonal numbers
        for(let i = 1; i <= n; i++)
        {
            summ += Centered_tridecagonal_num(i);
        }
        return summ ;
    }

    let n = 5;
    document.write(sum_Centered_tridecagonal_num(n));

 // This code is contributed by divyesh072019.
</script>

Output:

265

Time complexity: O(N).
Auxiliary Space: O(1) as it is using constant space for variables