Find the sum of the first N Centered Decagonal Numbers

Last Updated : 19 Sep, 2022

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

The first few Centered decagonal numbers are 1, 11, 31, 61, 101, 151 ...

Examples:

Input: N = 3
Output: 43
Explanation:
1, 11 and 31 are the first three Centered decagonal numbers.
Input: N = 5
Output: 205

Approach:

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

Below is the implementation of the above approach:

C++

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

// Function to find the N-th
// centered decagonal number
int Centered_decagonal_num(int n) 
{

    // Formula to calculate nth
    // centered_decagonal number
    // & return it into main function.
    return (5 * n * n - 5 * n + 1);
}

// Function to find the sum of
// the first N centered decagonal
// numbers
int sum_Centered_decagonal_num(int n)
{

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

    // Iterating through the range
    for(int i = 1; i < n + 1; i++)
    {
       summ += Centered_decagonal_num(i);
    }
    return summ;
}

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

    // Display first Nth 
    // centered_decagonal number
    cout << (sum_Centered_decagonal_num(n));

    return 0;
}

// This code is contributed by PrinciRaj1992

Java

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

    // Formula to calculate nth
    // centered_decagonal number
    // & return it into main function.
    return (5 * n * n - 5 * n + 1);
}

// Function to find the sum of
// the first N centered decagonal
// numbers
static int sum_Centered_decagonal_num(int n)
{

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

    // Iterating through the range
    for(int i = 1; i < n + 1; i++)
    {
       summ += Centered_decagonal_num(i);
    }
    return summ;
}

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

    // Display first Nth 
    // centered_decagonal number
    System.out.println(sum_Centered_decagonal_num(n));
}
}

// This code is contributed by sapnasingh4991

Python3

# Python3 program to find the sum of 
# the first N centered
# decagonal number

# Function to find the N-th 
# centered decagonal number
def Centered_decagonal_num(n): 

    # Formula to calculate  
    # nth Centered_decagonal 
    # number & return it 
    # into main function. 
    return (5 * n * n - 
            5 * n + 1) 
    
  
# Function to find the
# sum of the first N
# Centered decagonal 
# numbers 
def sum_Centered_decagonal_num(n) : 
    
    # Variable to store 
    # the sum
    summ = 0
    
    # Iterating through the range
    for i in range(1, n + 1):

        summ += Centered_decagonal_num(i)
    
    return summ
  
# Driver code 
if __name__ == '__main__' : 
          
    n = 5
    
    # display first Nth 
    # Centered_decagonal number
    print(sum_Centered_decagonal_num(n))

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

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

    // Formula to calculate nth
    // centered_decagonal number
    // & return it into main function.
    return (5 * n * n - 5 * n + 1);
}

// Function to find the sum of
// the first N centered decagonal
// numbers
static int sum_Centered_decagonal_num(int n)
{

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

    // Iterating through the range
    for(int i = 1; i < n + 1; i++)
    {
        summ += Centered_decagonal_num(i);
    }
    return summ;
}

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

    // Display first Nth 
    // centered_decagonal number
    Console.WriteLine(sum_Centered_decagonal_num(n));
}
}

// This code is contributed by sapnasingh4991

JavaScript

<script>

    // Javascript program to find the sum of the  
    // first N centered decagonal number 
    
    // Function to find the N-th 
    // centered decagonal number 
    function Centered_decagonal_num(n)  
    { 

        // Formula to calculate nth 
        // centered_decagonal number 
        // & return it into main function. 
        return (5 * n * n - 5 * n + 1); 
    } 

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

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

        // Iterating through the range 
        for(let i = 1; i < n + 1; i++) 
        { 
           summ += Centered_decagonal_num(i); 
        } 
        return summ; 
    } 
    
    let n = 5; 
  
    // Display first Nth  
    // centered_decagonal number 
    document.write(sum_Centered_decagonal_num(n)); 

</script>

Output:

Time Complexity: O(N).
Auxiliary Space: O(1) as it is using constant variables

Find the sum of the first N Centered Decagonal Numbers

SHUBHAMSINGH10

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Find the sum of the first N Centered Decagonal Numbers

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