Find the sum of the first Nth Centered Pentadecagonal Number

Last Updated : 30 Jan, 2023

Given a number N the task is to find the sum of the first N Centered Pentadecagonal Number.

The first few Centered Pentadecagonal Numbers are 1, 16, 46, 91, 151, 226, 316 ...

Examples:

Input: N = 3
Output: 63
Explanation:
1, 16 and 46 are the first three centered pentadecagonal numbers.

Input: N = 5
Output: 305

Approach:

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

Below is the implementation of the above approach:

C++

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

// Function to find the centered
// pentadecagonal number
int Centered_Pentadecagonal_num(int n)
{

    // Formula to calculate
    // N-th centered pentadecagonal
    // number
    return (15 * n * n - 15 * n + 2) / 2;
}

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

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

    for(int i = 1; i < n + 1; i++)
    {
       summ += Centered_Pentadecagonal_num(i);
    }
    return summ;
}

// Driver Code
int main()
{
    int n = 5;
    
    cout << sum_Centered_Pentadecagonal_num(n);
    return 0;
}

// This code is contributed by Rajput-Ji

Java

// Java program to find the sum of the
// first N centered pentadecagonal number
class GFG {
    
// Function to find the centered
// pentadecagonal number
static int Centered_Pentadecagonal_num(int n)
{

    // Formula to calculate
    // N-th centered pentadecagonal
    // number
    return (15 * n * n - 15 * n + 2) / 2;
}

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

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

    for(int i = 1; i < n + 1; i++)
    {
       summ += Centered_Pentadecagonal_num(i);
    }
    return summ;
}

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

    System.out.println(sum_Centered_Pentadecagonal_num(n));
}
}

// This code is contributed by sapnasingh4991

Python3

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

# Function to find the 
# Centered_Pentadecagonal 
# number 
def Centered_Pentadecagonal_num(n): 

    # Formula to calculate  
    # N-th Centered_Pentadecagonal 
    # number 
    return (15 * n * n - 
            15 * n + 2) // 2
    
  
# Function to find the 
# sum of the first N
# Centered_Pentadecagonal 
# numbers
def sum_Centered_Pentadecagonal_num(n) : 
    
    # Variable to store 
    # the sum
    summ = 0
    
    for i in range(1, n + 1):

        summ += Centered_Pentadecagonal_num(i)
    
    return summ
  
# Driver code 
if __name__ == '__main__' : 
          
    n = 5

    print(sum_Centered_Pentadecagonal_num(n))

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

class GFG 
{
    
// Function to find the centered
// pentadecagonal number
static int Centered_Pentadecagonal_num(int n)
{

    // Formula to calculate
    // N-th centered pentadecagonal
    // number
    return (15 * n * n - 15 * n + 2) / 2;
}

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

    // Variable to store
    // the sum
    int summ = 0;
    
    for(int i = 1; i < n + 1; i++)
    {
        summ += Centered_Pentadecagonal_num(i);
    }
    return summ;
}

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

    Console.WriteLine(sum_Centered_Pentadecagonal_num(n));
}
}

// This code is contributed by sapnasingh4991

JavaScript

<script>

    // Javascript program to find the sum of the 
    // first N centered pentadecagonal number 
    
    // Function to find the centered 
    // pentadecagonal number 
    function Centered_Pentadecagonal_num(n) 
    { 

        // Formula to calculate 
        // N-th centered pentadecagonal 
        // number 
        return (15 * n * n - 15 * n + 2) / 2; 
    } 

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

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

        for(let i = 1; i < n + 1; i++) 
        { 
           summ += Centered_Pentadecagonal_num(i); 
        } 
        return summ; 
    } 
    
    let n = 5; 
      
    document.write(sum_Centered_Pentadecagonal_num(n)); 

</script>

Output:

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

Find the sum of the first Nth Centered Pentadecagonal Number

SHUBHAMSINGH10

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Find the sum of the first Nth Centered Pentadecagonal Number

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