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Find the sum of the first Nth Centered Pentadecagonal Number
  • Last Updated : 17 Mar, 2021

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 Nth centred Pentadecagonal number. 
     
  2. Now, run a loop starting from 1 to N, to find ith 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)
 

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