Find the sum of the first N Centered Octadecagonal Numbers

Last Updated : 19 Sep, 2022

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

Input: N = 3
Output: 75
Explanation:
1, 19 and 55 are the first three centered octadecagonal numbers.
Input: N = 10
Output: 298

Approach:

Initially, we need to create a function which will help us to calculate the N^th centered octadecagonal number.
Now, run a loop starting from 1 to N, to find i^th centered octadecagonal numbers.
Add all the above calculated centered octadecagonal numbers.
Finally, display the sum of the first N centered octadecagonal numbers.

Below is the implementation of the above approach:

C++

// C++ program to find the sum of the 
// first N centered octadecagonal numbers
#include<bits/stdc++.h> 
using namespace std; 

// Function to find the N-th centered
// octadecagonal number
int center_octadecagon_num(int n)
{

    // Formula to calculate
    // nth centered octadecagonal
    // number
    return (9 * n * n - 9 * n + 1);
}

// Function to find the sum of the first
// N centered octadecagonal numbers
int sum_center_octadecagon_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_octadecagon_num(i);
    }
    return summ;
}

// Driver Code
int main()
{
    int n = 3;

    cout << (sum_center_octadecagon_num(n));
    return 0;
}

// This code is contributed by Rajput-Ji

Java

// Java program to find the sum of the  
// first N centered octadecagonal numbers
class GFG {
    
// Function to find the N-th centered
// octadecagonal number
static int center_octadecagon_num(int n)
{

    // Formula to calculate
    // nth centered octadecagonal
    // number
    return (9 * n * n - 9 * n + 1);
}

// Function to find the sum of the first
// N centered octadecagonal numbers
static int sum_center_octadecagon_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_octadecagon_num(i);
    }
    return summ;
}

// Driver Code
public static void main(String[] args)
{
    int n = 3;

    System.out.println(sum_center_octadecagon_num(n));
}
}

// This code is contributed by sapnasingh4991

Python3

# Python3 program to find the sum of 
# the first N Centered Octadecagonal 
# numbers

# Function to find the N-th
# Centered octadecagonal 
# number 
def center_octadecagon_num(n): 

    # Formula to calculate  
    # nth centered octadecagonal 
    # number
    return (9 * n * n - 9 * n + 1)
    
  
# Function to find the sum of 
# the first N Centered 
# octadecagonal numbers
def sum_center_octadecagon_num(n) : 
    
    # Variable to store 
    # the sum
    summ = 0
    
    # Iterating through the range 
    # 1 to N
    for i in range(1, n + 1):

        summ += center_octadecagon_num(i)
    
    return summ
  
# Driver code 
if __name__ == '__main__' : 
          
    n = 3
    
    print(sum_center_octadecagon_num(n))

// C# program to find the sum of the 
// first N centered octadecagonal numbers
using System;

class GFG {
    
// Function to find the N-th centered
// octadecagonal number
static int center_octadecagon_num(int n)
{

    // Formula to calculate
    // nth centered octadecagonal
    // number
    return (9 * n * n - 9 * n + 1);
}

// Function to find the sum of the first
// N centered octadecagonal numbers
static int sum_center_octadecagon_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_octadecagon_num(i);
    }
    return summ;
}

// Driver Code
public static void Main(String[] args)
{
    int n = 3;

    Console.WriteLine(sum_center_octadecagon_num(n));
}
}

// This code is contributed by sapnasingh4991

JavaScript

<script>
    // Javascript program to find the sum of the  
    // first N centered octadecagonal numbers 
    
    // Function to find the N-th centered 
    // octadecagonal number 
    function center_octadecagon_num(n) 
    { 

        // Formula to calculate 
        // nth centered octadecagonal 
        // number 
        return (9 * n * n - 9 * n + 1); 
    } 

    // Function to find the sum of the first 
    // N centered octadecagonal numbers 
    function sum_center_octadecagon_num(n) 
    { 

        // Variable to store 
        // the sum 
        let summ = 0; 

        // Iterating through the range 
        // 1 to N 
        for(let i = 1; i < n + 1; i++) 
        { 
            summ += center_octadecagon_num(i); 
        } 
        return summ; 
    } 
    
    let n = 3; 
    document.write(sum_center_octadecagon_num(n));

// This code is contributed by divyeshrabadiya07.
</script>

Output:

Time Complexity: O(N).

Auxiliary Space: O(1) since constant variables are being used

Find the sum of the first N Centered Octadecagonal Numbers

SHUBHAMSINGH10

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Find the sum of the first N Centered Octadecagonal Numbers

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