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Find the sum of the first Nth Icosidigonal Number
  • Last Updated : 18 Mar, 2021

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 Nth icosidigonal number.
  2. Now, run a loop starting from 1 to N, to find ith 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).
 

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