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Find the sum of the first N Centered Decagonal Numbers
  • Last Updated : 17 Mar, 2021

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 Nth Centered decagonal number.
  2. Now, run a loop starting from 1 to N, to find the ith 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 centred decagonal number
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the N-th
// centred 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 centred decagonal number
class GFG {
     
// Function to find the N-th
// centred 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 centred
# decagonal number
 
# Function to find the N-th
# centred 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 centred decagonal number
using System;
 
class GFG {
     
// Function to find the N-th
// centred 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 centred decagonal number
     
    // Function to find the N-th
    // centred 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).
 

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