求第一个第N个居中的五角形数的总和

给定数字N ，任务是找到第一个N个中心五角形数的总和。

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

例子：

Input: N = 3 
Output: 63 
Explanation: 
1, 16 and 46 are the first three centered pentadecagonal numbers.
Input: N = 5 
Output: 305 
 

方法：

1. 最初，我们需要创建一个函数，该函数将帮助我们计算第N^个居中的五边形数。
2. 现在，运行一个从1到N的循环，以找到^第i^个居中的五边形数。
3. 将所有以上计算的居中五角形数相加。
4. 最后，显示第一个N个居中的五边形数字的总和。

下面是上述方法的实现：

C++

// C++ program to find the sum of the
// first N centered pentadecagonal number
#include
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

 
    // 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));
 

输出：

305

时间复杂度： O(N)