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# Find the sum of the first Nth Centered Tridecagonal Numbers

• Last Updated : 18 Mar, 2021

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``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

 ``
Output:
`265`

Time complexity: O(N).

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