3-10-4

@Scare Crow I didn't found that the pattern came everytime to 3 on a turn.
Here is a testing level I have made (but I am short on time for now). I made it to test the behavior of R on the 10 steps path (initialy). The red bricks are the place where R turns depending on the step you block it (for step 3 and 8, the next should be 10 but the word is to large to place them...).
What's strange is that if you block R with a fixed block (not slidered like here) the pattern change on some steps...

@Scare Crow That's a good news! Do you plan to share your conclusions?

Hand written? You meant you worked with papers? Just kidding If you feel comfortable with that (and it's readable), feel free to do as you want
Maybe I will open a forum thread later about that as suggested in your level...

Your image doesn't show up here but no problem in the forum. I use imgur.com and choose the png picture format to share images in comments (everybody faces this question one day or another in here )
I really think we should open a special thread about this in the forum... Just I can't do that for now

if he can't continue the sequence,he will walk randomly. therefore there isn't a real sequence for the robot

@meko Thanks! I am writting a special thread in the forum about that. From what I see, you've got a 2/13 then 10/4/3 sequence. That's something intriguing... When we block with a draggable/slidered block it is not the same result then with a fixed (a hole, brick or stone) block.

For those who are interested, I have opened a special thread in the forum on the subject under the Bugs & Feature requests: Bugs [?] Movement sequences of a headless R Bot
Feel free to share and investigate on the subject !