第N个偶数斐波那契数

给定一个值n，找到第n个偶数斐波那契数。
例子 ：

Input  : n  = 3
Output : 34

Input  : n  = 4
Output : 144

Input : n = 7
Output : 10946

斐波那契数是以下整数序列中的数字。
0、1、1、2、3、5、8、13、21、34、55、89、144等。
其中按顺序给出任何数字：

Fn = Fn-1 + Fn-2 
      with seed values
      F0 = 0 and F1 = 1.

偶数斐波那契数列是0、2、8、34、144、610、2584…。我们需要按此顺序找到第n个数字。
如果我们仔细研究斐波那契数列，我们会注意到序列中的第三个数字都是偶数，偶数序列遵循以下递归公式。

Recurrence for Even Fibonacci sequence is:
     EFn = 4EFn-1 + EFn-2
with seed values
     EF0 = 0 and EF1 = 2.

EFn represents n'th term in Even Fibonacci sequence.

以上公式如何运作?
让我们看一下原始的斐波那契公式，并以Fn-3和Fn-6的形式编写它，因为事实上每三个斐波那契数都是偶数。

Fn = Fn-1 + Fn-2 [Expanding both terms]
   = Fn-2 + Fn-3 + Fn-3 + Fn-4 
   = Fn-2 + 2Fn-3 + Fn-4 [Expending first term]
   = Fn-3 + Fn-4 + 2Fn-3 + Fn-4
   = 3Fn-3 + 2Fn-4  [Expending one Fn-4]
   = 3Fn-3 + Fn-4 + Fn-5 + Fn-6 [Combing Fn-4 and Fn-5]
   = 4Fn-3 + Fn-6  

Since every third Fibonacci Number is even, So if Fn is 
even then Fn-3 is even and Fn-6 is also even. Let Fn be
xth even element and mark it as EFx.
If Fn is EFx, then Fn-3 is previous even number i.e. EFx-1
and Fn-6 is previous of EFx-1 i.e. EFx-2
So
Fn = 4Fn-3 + Fn-6
which means,
EFx = 4EFx-1 + EFx-2

C++

// C++ code to find Even Fibonacci
//Series using normal Recursion
#include
using namespace std;
 
// Function which return
//nth even fibonnaci number
long int evenFib(int n)
{
    if (n < 1)
    return n;
    if (n == 1)
    return 2;
 
    // calculation of
    // Fn = 4*(Fn-1) + Fn-2
    return ((4 * evenFib(n-1)) +
             evenFib(n-2));
}
 
// Driver Code
int main ()
{
    int n = 7;
    cout << evenFib(n);
    return 0;
}

Java

// Java code to find Even Fibonacci
// Series using normal Recursion
 
class GFG{
  
// Function which return
// nth even fibonnaci number
static long evenFib(int n)
{
    if (n < 1)
    return n;
 
    if (n == 1)
    return 2;
 
    // calculation of
    // Fn = 4*(Fn-1) + Fn-2
    return ((4 * evenFib(n-1)) +
                 evenFib(n-2));
}
 
// Driver Code
public static void main (String[] args)
{
    int n = 7;
    System.out.println(evenFib(n));
}
}
 
// This code is contributed by
// Smitha Dinesh Semwal

Python3

# Python3 code to find Even  Fibonacci
# Series using normal Recursion
  
# Function which return
#nth even fibonnaci number
def evenFib(n) :
    if (n < 1) :
        return n
    if (n == 1)  :
        return 2
  
    # calculation of
    # Fn = 4*(Fn-1) + Fn-2
    return ((4 * evenFib(n-1)) + evenFib(n-2)) 
 
 
# Driver Code
n = 7
print(evenFib(n))
 
 
# This code is contributed by Nikita Tiwari.

C#

// C# code to find Even Fibonacci
// Series using normal Recursion
using System;
 
class GFG {
 
// Function which return
// nth even fibonnaci number
static long evenFib(int n)
{
    if (n < 1)
    return n;
 
    if (n == 1)
    return 2;
 
    // calculation of Fn = 4*(Fn-1) + Fn-2
    return ((4 * evenFib(n - 1)) +
                 evenFib(n - 2));
}
 
// Driver code
public static void Main ()
{
    int n = 7;
    Console.Write(evenFib(n));
}
}
 
// This code is contributed by Nitin Mittal.

Javascript

// Javascript code to find Even Fibonacci
// Series using normal Recursion
 
// Function which return
// nth even fibonnaci number
function evenFib(n)
{
    if (n < 1)
        return n;
    if (n == 1)
        return 2;
 
    // calculation of
    // Fn = 4*(Fn-1) + Fn-2
    return ((4 * evenFib(n-1)) +
                 evenFib(n-2));
}
 
// Driver Code
let n = 7;
document.write(evenFib(n));
 
// This code is contributed by _saurabh_jaiswal.

输出 ：

10946