Find the sum of the first Nth Centered Tridecagonal Numbers

Last Updated : 19 Sep, 2022

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:

Initially, we need to create a function which will help us to calculate the N^th Centered tridecagonal number.
Now, Run a loop starting from 1 to N, and find the Centered tridecagonal numbers in this range.
Add all the above calculated Centered tridecagonal numbers.
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# 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:

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

Find the sum of the first Nth Centered Tridecagonal Numbers

SHUBHAMSINGH10

Improve

Article Tags :

Practice Tags :

Mathematical

Find the sum of the first Nth Centered Tridecagonal Numbers

Similar Reads

Thank You!

What kind of Experience do you want to share?