Find the sum of the first Nth Icosidigonal Number

Given a number N, the task is to find the sum of the first N Icosidigonal Numbers.

The first few Icosidigonal numbers are 1, 22, 63, 124, 205, 306 …

Examples:

Input: N = 3 
Output: 86 
Explanation:
1, 22 and 63 are the first three Icosidigonal numbers.
Input: N = 6 
Output: 721 

Approach:

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

Below is the implementation of the above approach: 

C++

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

// Function to find the
// N-th icosidigonal number
int Icosidigonal_num(int n)
{

    // Formula to calculate
    // nth icosidigonal number
    return (20 * n * n - 18 * n) / 2;
}

// Function to find the sum of the
// first N icosidigonal number
int sum_Icosidigonal_num(int n)
{

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

    // Iterating in the range 1 to N
    for(int i = 1; i < n + 1; i++)
    {

        // Finding the sum
        summ += Icosidigonal_num(i);
    }
    return summ;
}

// Driver code
int main()
{
    int n = 6;

    // Display first Nth
    // icosidigonal numbers
    cout << sum_Icosidigonal_num(n);
}

// This code is contributed by coder001

Java

// Java program to find the sum of the
// first N icosidigonal numbers
class GFG{

// Function to find the
// N-th icosidigonal number
public static int Icosidigonal_num(int n)
{

    // Formula to calculate
    // nth icosidigonal number
    return (20 * n * n - 18 * n) / 2;
}

// Function to find the sum of the
// first N icosidigonal number
public static int sum_Icosidigonal_num(int n)
{

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

    // Iterating in the range 1 to N
    for(int i = 1; i < n + 1; i++)
    {

       // Finding the sum
       summ += Icosidigonal_num(i);
    }
    return summ;
}

// Driver code
public static void main(String[] args)
{
    int n = 6;

    // Display first Nth
    // icosidigonal numbers
    System.out.println(sum_Icosidigonal_num(n));
}
}

// This code is contributed by divyeshrabadiya07

Python3

# Python3 program to find the
# sum of the first N
# Icosidigonal numbers

# Function to find the
# N-th Icosidigonal
# number
def Icosidigonal_num(n):

    # Formula to calculate
    # nth Icosidigonal
    # number
    return (20 * n * n -
            18 * n) // 2


# Function to find the
# sum of the first N
# Icosidigonal number
def sum_Icosidigonal_num(n) :

    # Variable to store
    # the sum
    summ = 0

    # Iterating in the range
    # 1 to N
    for i in range(1, n + 1):

        summ += Icosidigonal_num(i)

    return summ

# Driver code
if __name__ == '__main__' :

    n = 6


    print(sum_Icosidigonal_num(n))

C#

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

class GFG{

// Function to find the
// N-th icosidigonal number
static int Icosidigonal_num(int n)
{

    // Formula to calculate
    // nth icosidigonal number
    return (20 * n * n - 18 * n) / 2;
}

// Function to find the sum of the
// first N icosidigonal number
static int sum_Icosidigonal_num(int n)
{

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

    // Iterating in the range 1 to N
    for(int i = 1; i < n + 1; i++)
    {

       // Finding the sum
       summ += Icosidigonal_num(i);
    }
    return summ;
}

// Driver code
public static void Main(string[] args)
{
    int n = 6;

    // Display first Nth
    // icosidigonal numbers
    Console.WriteLine(sum_Icosidigonal_num(n));
}
}

// This code is contributed by AnkitRai01

Javascript

<script>
    // Javascript program to find the sum of the
    // first N icosidigonal numbers

    // Function to find the
    // N-th icosidigonal number
    function Icosidigonal_num(n)
    {

        // Formula to calculate
        // nth icosidigonal number
        return (20 * n * n - 18 * n) / 2;
    }

    // Function to find the sum of the
    // first N icosidigonal number
    function sum_Icosidigonal_num(n)
    {

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

        // Iterating in the range 1 to N
        for(let i = 1; i < n + 1; i++)
        {

            // Finding the sum
            summ += Icosidigonal_num(i);
        }
        return summ;
    }

    let n = 6;

    // Display first Nth
    // icosidigonal numbers
    document.write(sum_Icosidigonal_num(n));

// This code is contributed by divyesh072019.
</script>

Output:

721

Time complexity: O(N).

Auxiliary space: O(1) since it is using constant space for variables