Fibonacci and Bias

Why does the Fibonacci sequence display a bias towards odd numbers?

As the number of terms in the sequence gets larger and large, the ratio off odd terms to even terms approaches 2.

>>4
You might notice that the FS sequence you gave is exactly twice the original, since you started off with base cases that were twice in size.

Yes -> we can analyze by considering the finite cases mod 2

0,0 -> 0,0,0...
1,0 -> 1,1,0...
0,1 -> 1,0,1...
1,1 -> 0,1,1...

Thus, there will either be twice as many odds as evens, or no odds at all.

For moar phun,
define ø = [1+sqrt(5)]/2
[(ø^n)-(1-ø)^n]/sqrt(5) = F_n