Mathematical Thinking I, II, .... (previously Puzzle: Marrie

[Sayumi]

How about this:

Spoiler:

1
1 1
2 1
1 2 1 1
1 2 3 1
1 3 1 2 2 1

If this is correct anyone who wants to can out up the next one.... I'm kinda running out of ideas 

[c-square]

How about this:

Spoiler:

1
1 1
2 1
1 2 1 1
1 2 3 1
1 3 1 2 2 1

If this is correct anyone who wants to can out up the next one.... I'm kinda running out of ideas 

Nope!  Everyone's dancing around the right answer, but no one's hit it yet.

Let me give the next line and see if you can come up with the following two.

1
1 1
2 1
1 2 1 1
1 1 1 2 2 1

What are the next two lines after this?

[miakakiri]

Spoiler:

3 1 2 2 1 1
1 3 1 1 2 2 2 1
1 1 1 3 2 1 3 2 1 1
3 1 1 3 1 2 1 1 1 3 1 2 2 1
1 3 2 1 1 3 1 1 1 2 3 1 1 3 2 2 1 1
1 1 1 3 1 2 2 1 1 3 3 1 1 2 1 3 2 1 1 3 2 2 2 1

Oops, I went overboard. Once you see the pattern, it's really easy. I think I may have seen something like this a long time ago, which is how I got the pattern so easily.
Or am I doing it wrong?

[c-square]

Spoiler:

3 1 2 2 1 1
1 3 1 1 2 2 2 1
1 1 1 3 2 1 3 2 1 1
3 1 1 3 1 2 1 1 1 3 1 2 2 1
1 3 2 1 1 3 1 1 1 2 3 1 1 3 2 2 1 1
1 1 1 3 1 2 2 1 1 3 3 1 1 2 1 3 2 1 1 3 2 2 2 1

Oops, I went overboard. Once you see the pattern, it's really easy. I think I may have seen something like this a long time ago, which is how I got the pattern so easily.
Or am I doing it wrong?

Pin Pon!  Correct!  In case people think this isn't really a mathematical sequence, apparently someone has come up with a formula for calculating the next row based on the previous one.  It can be found here if you're interested!

Your turn, miakakiri!

[miakakiri]

Um.....Pass?
Sorry, I can't think of a puzzle right now. Someone else can have a turn.

I'm better at solving puzzles than posing them...~_~*