Find the sum of the first N Centered Decagonal Numbers

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:

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

// 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:

205

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