Even Fibonacci Numbers Sum

Given a limit, find the sum of all the even-valued terms in the Fibonacci sequence below given limit.

The first few terms of Fibonacci Numbers are, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ,… (Even numbers are highlighted).

Examples :

Input : limit = 8
Output : 10
Explanation : 2 + 8 = 10

Input : limit = 400;
Output : 188.
Explanation : 2 + 8 + 34 + 144 = 188.

A simple solution is to iterate through all prime numbers while the next number is less than or equal to given limit. For every number, check if it is even. If the number is even, add it to the result.

An efficient solution is based on the below recursive formula for even Fibonacci Numbers

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.

Refer this more details of above formula.

So while iterating over Fibonacci numbers, we only generate even Fibonacci numbers.

C++

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// Find the sum of all the even-valued terms in
// the Fibonacci sequence which do not exceed
// given limit.
#include<iostream>
using namespace std;
  
// Returns sum of even Fibonacci numbers which are
// less than or equal to given limit.
int evenFibSum(int limit)
{
    if (limit < 2)
        return 0;
  
    // Initialize first two even prime numbers
    // and their sum
    long long int ef1 = 0, ef2 = 2;
    long long int sum = ef1 + ef2;
  
    // calculating sum of even Fibonacci value
    while (ef2 <= limit)
    {
        // get next even value of Fibonacci sequence
        long long int ef3 = 4*ef2 + ef1;
  
        // If we go beyond limit, we break loop
        if (ef3 > limit)
            break;
  
        // Move to next even number and update sum
        ef1 = ef2;
        ef2 = ef3;
        sum += ef2;
    }
  
    return sum;
}
  
// Driver code
int main()
{
    int limit = 400;
    cout << evenFibSum(limit);
    return 0;
}

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Java

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// Find the sum of all the even-valued terms in
// the Fibonacci sequence which do not exceed
// given limit.
import java.io.*;
  
class GFG 
{
    // Returns sum of even Fibonacci numbers which are
    // less than or equal to given limit.
    static int evenFibSum(int limit)
    {
        if (limit < 2)
            return 0;
      
        // Initialize first two even prime numbers
        // and their sum
        long ef1 = 0, ef2 = 2;
        long sum = ef1 + ef2;
      
        // calculating sum of even Fibonacci value
        while (ef2 <= limit)
        {
            // get next even value of Fibonacci sequence
            long ef3 = 4 * ef2 + ef1;
      
            // If we go beyond limit, we break loop
            if (ef3 > limit)
                break;
      
            // Move to next even number and update sum
            ef1 = ef2;
            ef2 = ef3;
            sum += ef2;
        }
      
        return(int) sum;
    }
      
    // Driver code
    public static void main (String[] args) 
    {
        int limit = 400;
        System.out.println(evenFibSum(limit));
          
    }
}
  
// This code is contributed by vt_m.

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Python3

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# Find the sum of all the even-valued 
# terms in the Fibonacci sequence which 
# do not exceed given limit.
  
# Returns sum of even Fibonacci numbers which
# are less than or equal to given limit.
def evenFibSum(limit) :
    if (limit < 2) :
        return 0
  
    # Initialize first two even prime numbers
    # and their sum
    ef1 = 0
    ef2 = 2
    sm= ef1 + ef2
      
    # calculating sum of even Fibonacci value
    while (ef2 <= limit) :
  
        # get next even value of Fibonacci 
        # sequence
        ef3 = 4 * ef2 + ef1
  
        # If we go beyond limit, we break loop
        if (ef3 > limit) :
            break
  
        # Move to next even number and update
        # sum
        ef1 = ef2
        ef2 = ef3
        sm = sm + ef2
      
    return sm
  
# Driver code
limit = 400
print(evenFibSum(limit))
  
# This code is contributed by Nikita Tiwari.

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C#

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// C# program to Find the sum of all
// the even-valued terms in the 
// Fibonacci sequence which do not
// exceed given limit.given limit.
using System;
  
class GFG {
      
    // Returns sum of even Fibonacci 
    // numbers which are less than or
    // equal to given limit.
    static int evenFibSum(int limit)
    {
        if (limit < 2)
            return 0;
      
        // Initialize first two even
        // prime numbers and their sum
        long ef1 = 0, ef2 = 2;
        long sum = ef1 + ef2;
      
        // calculating sum of even 
        // Fibonacci value
        while (ef2 <= limit)
        {
              
            // get next even value of 
            // Fibonacci sequence
            long ef3 = 4 * ef2 + ef1;
      
            // If we go beyond limit,
            // we break loop
            if (ef3 > limit)
                break;
      
            // Move to next even number
            // and update sum
            ef1 = ef2;
            ef2 = ef3;
            sum += ef2;
        }
      
        return(int) sum;
    }
      
    // Driver code
    public static void Main () 
    {
        int limit = 400;
        Console.Write(evenFibSum(limit));
          
    }
}
  
// This code is contributed by Nitin Mittal.

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PHP

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<?php
// Find the sum of all the 
// even-valued terms in the 
// Fibonacci sequence which 
// do not exceed given limit.
  
// Returns sum of even Fibonacci
// numbers which are less than or 
// equal to given limit.
function evenFibSum($limit)
{
    if ($limit < 2)
        return 0;
  
    // Initialize first two even 
    // prime numbers and their sum
    $ef1 = 0; $ef2 = 2;
    $sum = $ef1 + $ef2;
  
    // calculating sum of
    // even Fibonacci value
    while ($ef2 <= $limit)
    {
        // get next even value of
        // Fibonacci sequence
        $ef3 = 4 * $ef2 + $ef1;
  
        // If we go beyond limit,
        // we break loop
        if ($ef3 > $limit)
            break;
  
        // Move to next even number
        // and update sum
        $ef1 = $ef2;
        $ef2 = $ef3;
        $sum += $ef2;
    }
  
    return $sum;
}
  
// Driver code
$limit = 400;
echo(evenFibSum($limit));
  
// This code is contributed by Ajit.
?>

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Output :

188

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