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Find the sum of the first N Centered Dodecagonal Number
• Last Updated : 17 Mar, 2021

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

The first few Centered Dodecagonal Numbers are 1, 13, 37, 73, 121, 181 …

Examples:

Input: N = 3
Output: 51
Explanation:
1, 13 and 37 are the first three centered Dodecagonal number.
Input: N = 5
Output: 245

Approach:

1. Initially, create a function which will help us to calculate the Nth Centered Dodecagonal number.
2. Run a loop starting from 1 to N, to find i-th Centered Dodecagonal number.
3. Add all the above calculated Centered Dodecagonal numbers.
4. Finally, display the sum of the first N Centered Dodecagonal numbers.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the sum``// of the first N Centred``// Dodecagonal number``#include ``using` `namespace` `std;` `// Function to find the N-th ``// Centered Dodecagonal number``int` `Centered_Dodecagonal_num(``int` `n)``{``    ` `    ``// Formula to calculate nth ``    ``// Centered_Dodecagonal number``    ``return` `6 * n * (n - 1) + 1;``}` `// Function to find the sum of the first``// N Centered_Dodecagonal number``int` `sum_Centered_Dodecagonal_num(``int` `n)``{``    ` `    ``// Variable to store the sum``    ``int` `summ = 0;``    ` `    ``// Iterating from 1 to N``    ``for``(``int` `i = 1; i < n + 1; i++)``    ``{` `       ``// Finding the sum``       ``summ += Centered_Dodecagonal_num(i);``    ``}``    ``return` `summ;``}` `// Driver code``int` `main()``{``    ``int` `n = 5;``    ` `    ``cout << sum_Centered_Dodecagonal_num(n);``}` `// This code is contributed by coder001`

## Java

 `// Java program to find the sum of the ``// first N centred dodecagonal number``class` `GFG {``    ` `// Function to find the N-th``// centered dodecagonal number``static` `int` `Centered_Dodecagonal_num(``int` `n)``{``        ` `    ``// Formula to calculate nth``    ``// Centered_Dodecagonal number``    ``return` `6` `* n * (n - ``1``) + ``1``;``}``    ` `// Function to find the sum of the first``// N Centered_Dodecagonal number``static` `int` `sum_Centered_Dodecagonal_num(``int` `n)``{``        ` `    ``// Variable to store the sum``    ``int` `summ = ``0``;``        ` `    ``// Iterating from 1 to N``    ``for``(``int` `i = ``1``; i < n + ``1``; i++)``    ``{``        ` `       ``// Finding the sum``       ``summ += Centered_Dodecagonal_num(i);``    ``}``    ``return` `summ;``}``    ` `// Driver code``public` `static` `void` `main (String[] args)``{``    ``int` `n = ``5``;``        ` `    ``System.out.print(sum_Centered_Dodecagonal_num(n));``}``}` `// This code is contributed by AnkitRai01`

## Python3

 `# Python3 program to find the sum``# of the first N centred``# Dodecagonal number` `# Function to find the``# N-th Centered Dodecagonal``# number``def` `Centered_Dodecagonal_num(n):` `    ``# Formula to calculate ``    ``# nth Centered_Dodecagonal``    ``# number``    ``return` `6` `*` `n ``*` `(n ``-` `1``) ``+` `1``    ` `  ` `# Function to find the``# sum of the first N``# Centered_Dodecagonal``# number``def` `sum_Centered_Dodecagonal_num(n) :``    ` `    ``# Variable to store the``    ``# sum``    ``summ ``=` `0``    ` `    ``# Iterating from 1 to N``    ``for` `i ``in` `range``(``1``, n ``+` `1``):` `        ``# Finding the sum``        ``summ ``+``=` `Centered_Dodecagonal_num(i)``    ` `    ``return` `summ``  ` `# Driver code``if` `__name__ ``=``=` `'__main__'` `:``          ` `    ``n ``=` `5``    ` `    ``print``(sum_Centered_Dodecagonal_num(n))`

## C#

 `// C# program to find the sum of the``// first N centred dodecagonal number``using` `System;` `class` `GFG{``    ` `// Function to find the N-th``// centered dodecagonal number``static` `int` `Centered_Dodecagonal_num(``int` `n)``{``        ` `    ``// Formula to calculate nth``    ``// Centered_Dodecagonal number``    ``return` `6 * n * (n - 1) + 1;``}``    ` `// Function to find the sum of the first``// N Centered_Dodecagonal number``static` `int` `sum_Centered_Dodecagonal_num(``int` `n)``{``        ` `    ``// Variable to store the sum``    ``int` `summ = 0;``        ` `    ``// Iterating from 1 to N``    ``for``(``int` `i = 1; i < n + 1; i++)``    ``{``       ` `       ``// Finding the sum``       ``summ += Centered_Dodecagonal_num(i);``    ``}``    ``return` `summ;``}``    ` `// Driver code``public` `static` `void` `Main()``{``    ``int` `n = 5;``        ` `    ``Console.Write(sum_Centered_Dodecagonal_num(n));``}``}` `// This code is contributed by Code_Mech`

## Javascript

 ``
Output:
`245`

Time Complexity: O(N).

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