二阶欧拉数

d阶欧拉数序列可以表示为

1, 0, 0, 2, 8, 22, 52, 114, 240, 494, 1004, …..

第N个学期

给定整数N。任务是找到给定级数的第N个项。
例子：

Input: N = 0 
Output: 1 
$0^{th}$term = 1
Input: N = 4 
Output: 8 
 

方法：想法是找到二阶欧拉数的通用项。以下是二阶欧拉数的通用项的计算：

0th term = 2⁰ – 2*0 = 1 
1st Term = 2¹ – 2*1 = 0 
2nd term = 2² – 2*2 = 0 
3rd term = 2³ – 2*3 = 2 
4th term = 2⁴ – 2*4 = 8 
5th term = 2⁵ – 2*5 = 22 
. 
. 
. 
Nth term = 2ⁿ – 2*n. 
Therefore, the Nth term of the series is given as $2^n - 2*n$
 

下面是上述方法的实现：

C++

// C++ implementation to
// find N-th term in the series
 
#include 
#include 
using namespace std;
 
// Function to find N-th term
// in the series
void findNthTerm(int n)
{
    cout << pow(2, n) - 2 * n << endl;
}
 
// Driver Code
int main()
{
    int N = 4;
    findNthTerm(N);
 
    return 0;
}

Java

// Java implementation to find
// N-th term in the series
class GFG{
 
// Function to find N-th term
// in the series
static void findNthTerm(int n)
{
    System.out.println(Math.pow(2, n) - 2 * n);
}
 
// Driver code
public static void main(String[] args)
{
    int N = 4;
    findNthTerm(N);
}
}
 
// This code is contributed by Pratima Pandey

Python3

# Python3 implementation to
# find N-th term in the series
 
# Function to find N-th term
# in the series
def findNthTerm(n):
 
    print(pow(2, n) - 2 * n);
 
# Driver Code
N = 4;
findNthTerm(N);
 
# This code is contributed by Code_Mech

C#

// C# implementation to find
// N-th term in the series
using System;
class GFG{
 
// Function to find N-th term
// in the series
static void findNthTerm(int n)
{
    Console.Write(Math.Pow(2, n) - 2 * n);
}
 
// Driver code
public static void Main()
{
    int N = 4;
    findNthTerm(N);
}
}
 
// This code is contributed by Code_Mech

Javascript

 
// Javascript implementation to
// find N-th term in the series
 
// Function to find N-th term
// in the series
function findNthTerm(n)
{
    document.write((Math.pow(2, n)) - (2 * n));
}
 
// Driver Code
N = 4;
findNthTerm(N);
 

输出：

8

参考： OEIS