Find the sum of the first Nth Centered Pentadecagonal Number

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:

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

// 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:

305

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