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Find the sum of the first Nth Centered Tridecagonal Numbers

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  • Last Updated : 19 Sep, 2022
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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 Nth 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
 


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