Find the sum of the first N Centered Octadecagonal Numbers

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:

1. Initially, we need to create a function which will help us to calculate the N^th centered octadecagonal number.
2. Now, run a loop starting from 1 to N, to find i^th centered octadecagonal numbers.
3. Add all the above calculated centered octadecagonal numbers.
4. 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#

// 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:

75

Time Complexity: O(N).

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