求第N个居中的三边形数字的总和

给定一个数N ，任务是找到第一个N个居中的三边形数的总和。

A Centered tridecagonal number represents a dot at the center and other dots surrounding the center dot in the successive tridecagonal(13 sided polygon) layer. The first few Centered tridecagonal numbers are 1, 14, 40, 79 … 
 

例子：

Input: N = 3 
Output: 55 
Explanation: 
1, 14 and 40 are the first three Centered tridecagonal number. 
1 + 14 + 40 = 55.
Input: N = 5 
Output: 265 
 

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^个居中的十三边形数。
2. 现在，运行一个从1到N的循环，并在此范围内找到居中的三边形数字。
3. 将所有以上计算的居中三边形数字相加。
4. 最后，显示前N个居中的三边形数字的总和。

下面是上述方法的实现：

C++

// C++ program to find the sum of
// the first Nth centered
// tridecagonal number
#include
using namespace std;
 
// Function to calculate the
// N-th centered tridecagonal
// number
int Centered_tridecagonal_num(int n)
{
    // Formula to calculate
    // Nth centered tridecagonal
    // number & return it
    return (13 * n * (n - 1) + 2) / 2;
}
     
// Function to find the sum
// of the first N centered
// tridecagonal numbers
int sum_Centered_tridecagonal_num(int n)
{
    // Variable to store
    // the sum
    int summ = 0;
         
    // Loop to iterate and find the
    // sum of first N centered
    // tridecagonal numbers
    for(int i = 1; i <= n; i++)
    {
        summ += Centered_tridecagonal_num(i);
    }
    return summ ;
}
 
// Driver code
int main()
{
    int n = 5;
     
    cout << sum_Centered_tridecagonal_num(n)
         << endl;
    return 0;
}
 
// This code is contributed by rutvik_56

Java

// Java program to find the sum of
// the first Nth centered
// tridecagonal number
class GFG{
     
// Function to calculate the
// N-th centered tridecagonal
// number
public static int Centered_tridecagonal_num(int n)
{
     
    // Formula to calculate
    // Nth centered tridecagonal
    // number & return it
    return (13 * n * (n - 1) + 2) / 2;
}
     
// Function to find the sum
// of the first N centered
// tridecagonal numbers
public static int sum_Centered_tridecagonal_num(int n)
{
     
    // Variable to store
    // the sum
    int summ = 0;
         
    // Loop to iterate and find the
    // sum of first N centered
    // tridecagonal numbers
    for(int i = 1; i <= n; i++)
    {
       summ += Centered_tridecagonal_num(i);
    }
    return summ ;
}
 
// Driver code   
public static void main(String[] args)
{
    int n = 5;
     
    System.out.println(sum_Centered_tridecagonal_num(n));
}
}
 
// This code is contributed by divyeshrabadiya07

Python3

# Program to find the sum of
# the first Nth 
# Centered_tridecagonal number
 
# Function to calculate the
# N-th Centered tridecagonal
# number
def Centered_tridecagonal_num(n):
 
    # Formula to calculate 
    # Nth Centered tridecagonal
    # number & return it
    return (13 * n *
           (n - 1) + 2) // 2
     
   
# Function to find the sum
# of the first N
# Centered tridecagonal
# numbers
def sum_Centered_tridecagonal_num(n) :
     
    # Variable to store
    # the sum
    summ = 0
     
    # Loop to iterate and find the
    # sum of first N Centered
    # tridecagonal numbers
    for i in range(1, n + 1):
 
         
        summ += Centered_tridecagonal_num(i)
     
    return summ
   
# Driver Code
if __name__ == '__main__' :
           
    n = 5
 
    print(sum_Centered_tridecagonal_num(n))

C#

// C# program to find the sum of
// the first Nth centered
// tridecagonal number
using System;
 
class GFG{
     
// Function to calculate the
// N-th centered tridecagonal
// number
public static int Centered_tridecagonal_num(int n)
{
     
    // Formula to calculate
    // Nth centered tridecagonal
    // number & return it
    return (13 * n * (n - 1) + 2) / 2;
}
     
// Function to find the sum
// of the first N centered
// tridecagonal numbers
public static int sum_Centered_tridecagonal_num(int n)
{
     
    // Variable to store
    // the sum
    int summ = 0;
         
    // Loop to iterate and find the
    // sum of first N centered
    // tridecagonal numbers
    for(int i = 1; i <= n; i++)
    {
       summ += Centered_tridecagonal_num(i);
    }
    return summ;
}
 
// Driver code
public static void Main()
{
    int n = 5;
     
    Console.WriteLine(sum_Centered_tridecagonal_num(n));
}
}
 
// This code is contributed by Code_Mech

Javascript

 
    // Javascript program to find the sum of 
    // the first Nth centered
    // tridecagonal number   
     
    // Function to calculate the 
    // N-th centered tridecagonal 
    // number 
    function Centered_tridecagonal_num(n)
    {
     
        // Formula to calculate 
        // Nth centered tridecagonal 
        // number & return it 
        return (13 * n * (n - 1) + 2) / 2;
    }
 
    // Function to find the sum 
    // of the first N centered
    // tridecagonal numbers 
    function sum_Centered_tridecagonal_num(n)
    {
     
        // Variable to store 
        // the sum 
        let summ = 0;
 
        // Loop to iterate and find the 
        // sum of first N centered 
        // tridecagonal numbers 
        for(let i = 1; i <= n; i++)
        {
            summ += Centered_tridecagonal_num(i); 
        }
        return summ ;
    }
     
    let n = 5;       
    document.write(sum_Centered_tridecagonal_num(n));
  
 // This code is contributed by divyesh072019.

输出：

265

时间复杂度： O(N)。