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How many ways can the 2x2n (tube) board be tiled or filled with Tetris Pieces ? This is similar to other tilings except the Tetris pieces have 4 squares and have more complex configurations. The proof is a similar use of Recurrence equations then more simpler Polyominos. It has not been added to this math problem data base so thought we should add it. The reccurance is Fn^2

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    $\begingroup$ What math problem data base do you mean? And what answer do you have for $2 \times n$ board? Why is it a tube? are the ends joined somehow to make a donut shape? Might be good to list the Tetris shapes... $\endgroup$ – coffeemath Oct 25 '18 at 21:08
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    $\begingroup$ so far u are the only one to not understand my language . the term tube is used since i think of it as more of a tube then a board if its placed vertical that is and pieces fall into it lile tetris . why would u think ends are joined is a better question . and math problem data base means here ! .math stack exchange or when the name changes someday , mdbe ..math data base exchange . Lastly everyone knows what tetris pieces lool like . when u attack this problem u will end up drawing them and as a hint u will actually only end up drawing 4 ' kinds ' of the tetris shapes . good luck 😀👍 $\endgroup$ – Randin Oct 26 '18 at 19:27
  • $\begingroup$ Randin-- thanks for the clarifications. I agree I could have looked up tetris pieces, and was really only confused about the tube idea, and reference to math data base which I thought was a source other than this site. $\endgroup$ – coffeemath Oct 26 '18 at 20:06
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    $\begingroup$ coffeemath no problem ( but this one is ..get it ? 🤓) jokes aside this problem is interesting because the same method to solve it is , solves both the more complex polyominos beyond the tetromino ( tetris pieces ) , to the simpler ones ! i will try and attach link to the simpler case in my next comment , and as u know solving an easier case in math helps u conquer the bigger more complex cases 👍 $\endgroup$ – Randin Oct 27 '18 at 7:24
  • $\begingroup$ It looks like you have found a proof of some kind for the number of ways to tile the $2 \times n$ board... is it a recurrence or a formula? If not too involved it would be nice to put it in the question. $\endgroup$ – coffeemath Oct 27 '18 at 8:00

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