Find the sum of the first Nth Icosagonal Numbers

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

The first few Icosagonal numbers are 1, 20, 57, 112, 185, 276…

Examples:

Input: N = 3 
Output: 78 
Explanation:
1, 20 and 57 are the first three 
Icosagonal number.
Input: N = 5 
Output: 375 

Approach:

1. Initially, we need to create a function which will help us to calculate the N-th Icosagonal number.
2. Now, Run a loop starting from 1 to N, to find the sum of all the Icosagonal number.
3. Now, add all the above calculated Icosagonal numbers.
4. Finally, display the sum of 1st N Icosagonal numbers.

Below is the implementation of the above approach: 

C++

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

// Function to calculate the
// N-th icosagonal number
int Icosagonal_num(int n)
{
    // Formula to calculate
    // nth icosagonal number
    // & return it
    return (18 * n * n - 16 * n) / 2;
}

// Function to find the
// sum of the first N
// icosagonal numbers
int sum_Icosagonal_num(int n)
{
    // Variable to store
    // the sum
    int summ = 0;

    // Loop to iterate through
    // the first N values and
    // find the sum of first N
    // icosagonal numbers
    for(int i = 1; i <= n; i++)
    {

        // Function to get the
        // Icosagonal_num
        summ += Icosagonal_num(i);
    }
    return summ;
}

// Driver code
int main()
{
    int n = 5;

    // Display the sum of
    // first N icosagonal number
    cout << sum_Icosagonal_num(n) << endl;
}

// This code is contributed by rutvik_56

Java

// Java program to find the sum of
// the first N icosagonal number
class GFG{

// Function to calculate the
// N-th icosagonal number
public static int Icosagonal_num(int n)
{

    // Formula to calculate
    // nth icosagonal number
    // & return it
    return (18 * n * n - 16 * n) / 2;
}

// Function to find the
// sum of the first N
// icosagonal numbers
public static int sum_Icosagonal_num(int n)
{

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

    // Loop to iterate through
    // the first N values and
    // find the sum of first N
    // icosagonal numbers
    for(int i = 1; i <= n; i++)
    {

       // Function to get the
       // Icosagonal_num
       summ += Icosagonal_num(i);
    }
    return summ;
}

// Driver code
public static void main(String[] args)
{
    int n = 5;

    // Display the sum of
    // first N icosagonal number
    System.out.println(sum_Icosagonal_num(n));
}
}

// This code is contributed by divyeshrabadiya07

Python3

# Python program to find the
# sum of the first N
# Icosagonal number

# Function to calculate the
# N-th Icosagonal number
def Icosagonal_num(n):

    # Formula to calculate
    # nth Icosagonal
    # number & return it
    return (18 * n * n -
            16 * n) // 2


# Function to find the
# sum of the first N
# Icosagonal numbers
def sum_Icosagonal_num(n) :

    # Variable to store
    # the sum
    summ = 0

    # Loop to iterate through
    # the first N values and
    # find the sum of first N
    # Icosagonal numbers
    for i in range(1, n + 1):

        # function to get the
        # Icosagonal_num
        summ += Icosagonal_num(i)

    return summ

# Driver Code
if __name__ == '__main__' :

    n = 5

    # Display the sum of
    # first N Icosagonal number
    print(sum_Icosagonal_num(n))

C#

// C# program to find the sum of
// the first N icosagonal number
using System;

class GFG{

// Function to calculate the
// N-th icosagonal number
public static int Icosagonal_num(int n)
{

    // Formula to calculate
    // nth icosagonal number
    // & return it
    return (18 * n * n - 16 * n) / 2;
}

// Function to find the
// sum of the first N
// icosagonal numbers
public static int sum_Icosagonal_num(int n)
{

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

    // Loop to iterate through
    // the first N values and
    // find the sum of first N
    // icosagonal numbers
    for(int i = 1; i <= n; i++)
    {

       // Function to get the
       // Icosagonal_num
       summ += Icosagonal_num(i);
    }
    return summ;
}

// Driver code
public static void Main()
{
    int n = 5;

    // Display the sum of
    // first N icosagonal number
    Console.WriteLine(sum_Icosagonal_num(n));
}
}

// This code is contributed by Code_Mech

Javascript

<script>

    // Javascript program to find the sum of
      // the first N icosagonal number

    // Function to calculate the
    // N-th icosagonal number
    function Icosagonal_num(n)
    {
        // Formula to calculate
        // nth icosagonal number
        // & return it
        return (18 * n * n - 16 * n) / 2;
    }

    // Function to find the
    // sum of the first N
    // icosagonal numbers
    function sum_Icosagonal_num(n)
    {
        // Variable to store
        // the sum
        let summ = 0;

        // Loop to iterate through
        // the first N values and
        // find the sum of first N
        // icosagonal numbers
        for(let i = 1; i <= n; i++)
        {

            // Function to get the
            // Icosagonal_num
            summ += Icosagonal_num(i);
        }
        return summ;
    }

      let n = 5;

    // Display the sum of
    // first N icosagonal number
    document.write(sum_Icosagonal_num(n));

</script>

Output:

375

Time complexity: O(N)

Auxiliary Space: O(1) since constant space for variables is used

Another Approach:

1. Define a function icosagonal that takes an integer n and returns the nth icosagonal number using the formula n * (9 * n – 7).
2. Define a function sum_icosagonal that takes an integer n and returns the sum of the first n icosagonal numbers by calling icosagonal function for each number from 1 to n and adding up the results.
3. In main function, set the value of n to 5.
4. Call sum_icosagonal function with n as argument to calculate the sum of the first 5 icosagonal numbers.
5. Print the result using printf function.

C

#include <stdio.h>

int icosagonal(int n) {
    return n * (9 * n - 8);
}

int sum_icosagonal(int n) {
    int sum = 0;
    for (int i = 1; i <= n; i++) {
        sum += icosagonal(i);
    }
    return sum;
}

int main() {
    int n = 5;  // set the value of n to 5
    int sum = sum_icosagonal(n);
    printf("The sum of the first %d icosagonal numbers is %d\n", n, sum);
    return 0;
}

C++

#include <bits/stdc++.h>
using namespace std;
int icosagonal(int n) {
    return n * (9 * n - 8);
}

int sum_icosagonal(int n) {
    int sum = 0;
    for (int i = 1; i <= n; i++) {
        sum += icosagonal(i);
    }
    return sum;
}

int main() {
    int n = 5;  // set the value of n to 5
    int sum = sum_icosagonal(n);
      cout<<"The sum of the first "<<n<<" icosagonal numbers is "<<sum<<endl;
    return 0;
}

Python3

# Python program to find the sum
# of first n icosagonal numbers

# function to find icosagonal
# numbers
def icosagonal(n):
    return n * (9 * n - 8)

# function to find
# sum of n icosagonal
# numbers
def sum_icosagonal(n):
    _sum = 0

    for i in range(1,n+1):
        _sum += icosagonal(i)

    return _sum

# Driver Code
n = 5

# Storing the result
res = sum_icosagonal(n)

# Printing the result
print("The sum of first ",n," icosagonal Numbers is ",res)

# This code is contributed by - Dwaipayan Bandyopadhyay

Java

import java.io.*;

class GFG {
public static int icosagonal(int n) {
    return n * (9 * n - 8);
}

public static int sum_icosagonal(int n) {
    int sum = 0;
    for (int i = 1; i <= n; i++) {
        sum += icosagonal(i);
    }
    return sum;
}

public static void main (String[] args) {
    int n = 5;  // set the value of n to 5
    int sum = sum_icosagonal(n);
      System.out.print("The sum of the first " +n);
      System.out.print( " icosagonal numbers is " +sum);
}
}


// This code is contributed by shivanisinghss2110

Javascript

// Javascript code addition

// function to find icosagonal numbers
function icosagonal(n) {
  return n * (9 * n - 8);
}

// function to find sum of n icosagonal numbers
function sum_icosagonal(n) {
  let sum = 0;
  for (let i = 1; i <= n; i++) {
    sum += icosagonal(i);
  }
  return sum;
}

// Driver code
const n = 5;

// Storing the result
const res = sum_icosagonal(n);

// Printing the result
console.log(`The sum of first ${n} icosagonal numbers is ${res}`);

// The code is contributed by Nidhi goel.

C#

using System;

class Program {
    static int icosagonal(int n) {
        return n * (9 * n - 8);
    }

    static int sum_icosagonal(int n) {
        int sum = 0;
        for (int i = 1; i <= n; i++) {
            sum += icosagonal(i);
        }
        return sum;
    }

    static void Main() {
        int n = 5;  // set the value of n to 5
        int sum = sum_icosagonal(n);
        Console.WriteLine("The sum of the first {0} icosagonal numbers is {1}", n, sum);
    }
}

Output

The sum of the first 5 icosagonal numbers is 375

The time complexity of this program is O(n), where n is the input value.
 The space complexity is O(1) because we only need to store a few variables in memory.