Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with $1$ and $2$ , the first $10$ terms will be: $1,2,3,5,8,13,21,34,55,89...$

By considering the terms in the Fibonacci sequence whose values do not exceed four milliom, find the sum of the even-valued terms.

Here is the beginning of the Fibonacci sequence with even number in quotes:

$1 \ \ 1 \ \ "2" \ \ 3 \ \ 5 \ \ "8" \ \ 13 \ \ 21 \ \ "34" \ \ 55 \ \ 89 \ \ "144"$

$a \ \ b \ \ "c" \ \ a \ \ b \ \ "c" \ \ a \ \ b \ \ "c" \ \ a \ \ b \ \ "c"$

Every third number in Fibonacci sequence is even.

The even numbers of the sequence follows :

$E(n) = 4 \times E(n-1) + E(n-2)$ Sum them all and we have our answer

Answer : $4613732$