Pascal’s triangle is an awesome thing in mathematics that starts like this:
and is discussed more here:
Can you make one of the rows of Pascal’s triangle with TT?
Here is a go at the 1-3-3-1 row:
(click “Trigger Left” first)
where the integers 1-3-3-1 are encoded in the “registers” at the bottom half of the board, rather than using the colors of the marbles, although a solution using the color of marbles would be cool too.
The sum of the entries on one row of Pascal’s triangle sums to a power of two. It might be possible to get the 1-4-6-4-1 row with TT or maybe even bigger rows.