Permanently self-modifying code
Bash, 52 47 (49-2) bytes
EDITS:

Saved 5 bytes, by starting with 1 instead of 0. Thanks @Leo !

Golfed
A=$[1+0]
echo $A
sed -ri &quot;s/\w+\+(\w+)/\1+$A/&quot; $0

Test
&gt;for i in `seq 10`
&gt; do
&gt; ./fibo
&gt; done
1
1
2
3
5
8
13
21
34
55