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Find the sum of the first N Centered heptagonal number
• Last Updated : 17 Mar, 2021

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

The first few Centered heptagonal number are 1, 8, 22, 43, 71, 106, 148, …

Examples:

Input: N = 3
Output: 31
Explanation:
1, 8 and 22 are the first three centered heptagonal numbers.
Input: N = 5
Output: 145

Approach:

1. Initially, we need to create a function which will help us to calculate the Nth centered heptagonal number.
2. Now, run a loop starting from 1 to N, to find ith centered heptagonal number.
3. Add all the above calculated centered heptagonal numbers.
4. Finally, display the sum of the first N centered heptagonal numbers.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the sum of the``// first N centered heptagonal numbers``#include``using` `namespace` `std;` `// Function to find the N-th centered``// heptagonal number``int` `center_heptagonal_num(``int` `n)``{` `    ``// Formula to calculate``    ``// nth centered heptagonal``    ``// number``    ``return` `(7 * n * n - 7 * n + 2) / 2;``}` `// Function to find the sum of the first``// N centered heptagonal numbers``int` `sum_center_heptagonal_num(``int` `n)``{` `    ``// Variable to store``    ``// the sum``    ``int` `summ = 0;` `    ``// Iterating through the range``    ``// 1 to N``    ``for``(``int` `i = 1; i < n + 1; i++)``    ``{``       ``summ += center_heptagonal_num(i);``    ``}``    ``return` `summ;``}` `// Driver Code``int` `main()``{``    ``int` `n = 5;` `    ``cout << (sum_center_heptagonal_num(n));``    ``return` `0;``}` `// This code is contributed by PratikBasu`

## Java

 `// Java program to find the sum of the``// first N centered heptagonal numbers``class` `GFG{``    ` `// Function to find the N-th centered``// heptagonal number``public` `static` `int` `center_heptagonal_num(``int` `n)``{` `    ``// Formula to calculate``    ``// nth centered heptagonal``    ``// number``    ``return` `(``7` `* n * n - ``7` `* n + ``2``) / ``2``;``}` `// Function to find the sum of the first``// N centered heptagonal numbers``public` `static` `int` `sum_center_heptagonal_num(``int` `n)``{` `    ``// Variable to store``    ``// the sum``    ``int` `summ = ``0``;` `    ``// Iterating through the range``    ``// 1 to N``    ``for``(``int` `i = ``1``; i < n + ``1``; i++)``    ``{``        ``summ += center_heptagonal_num(i);``    ``}``    ``return` `summ;``}` `// Driver Code``public` `static` `void` `main(String args[])``{``    ``int` `n = ``5``;` `    ``System.out.print(sum_center_heptagonal_num(n));``}``}` `// This code is contributed by Code_Mech`

## Python3

 `# Python3 program to find the sum``# of the first N centered``# heptagonal numbers` `# Function to find N-th``# centered heptagonal``# number``def` `center_heptagonal_num(n):`` ` `    ``# Formula to calculate ``    ``# nth centered heptagonal``    ``# number``    ``return` `(``7` `*` `n ``*` `n ``-` `7` `*` `n ``+` `2``) ``/``/` `2``    ` `  ` `# Function to find the``# sum of the first N``# centered heptagonal``# numbers``def` `sum_center_heptagonal_num(n) :``    ` `    ``# Variable to store``    ``# the sum``    ``summ ``=` `0``    ` `    ``# Iterate through the range``    ``# 1 to N``    ``for` `i ``in` `range``(``1``, n ``+` `1``):``        ``summ ``+``=` `center_heptagonal_num(i)``    ` `    ``return` `summ``  ` `# Driver code``if` `__name__ ``=``=` `'__main__'` `:``          ` `    ``n ``=` `5``    ` `    ``print``(sum_center_heptagonal_num(n))`

## C#

 `// C# program to find the sum of the``// first N centered heptagonal numbers``using` `System;` `class` `GFG{``    ` `// Function to find the N-th centered``// heptagonal number``public` `static` `int` `center_heptagonal_num(``int` `n)``{` `    ``// Formula to calculate``    ``// nth centered heptagonal``    ``// number``    ``return` `(7 * n * n - 7 * n + 2) / 2;``}` `// Function to find the sum of the first``// N centered heptagonal numbers``public` `static` `int` `sum_center_heptagonal_num(``int` `n)``{` `    ``// Variable to store``    ``// the sum``    ``int` `summ = 0;` `    ``// Iterating through the range``    ``// 1 to N``    ``for``(``int` `i = 1; i < n + 1; i++)``    ``{``       ``summ += center_heptagonal_num(i);``    ``}``    ``return` `summ;``}` `// Driver Code``public` `static` `void` `Main()``{``    ``int` `n = 5;` `    ``Console.Write(sum_center_heptagonal_num(n));``}``}` `// This code is contributed by Akanksha_Rai`

## Javascript

 `` `// This code is contributed by divyeshrabadiya07.`
Output:
`145`

Time Complexity: O(N).

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