There are two triominoes. One is simple a 1x3 rectangle and the other is a small
L-shaped piece.
Using any combination of these two triominoes and in any orientation, how many ways can a 3 by N rectangle be tiled?
Rotations and reflections of an asymmetrical solution are to be considered distinct.
Thanks - it was a fun puzzle. (The last tiling I tried as a puzzle here led me to post in the OEIS - perplexus 11394 --> A316535).
While this one was covered by A134438, the Kreweras 1995 paper therein was fascinating (once I translated it to English). 1) it gave a proof as to why the list of tilings (2 oddballs and 3 infinite sets) is complete 2) It collapsed the recursion using generating functions in a way I still don't understand - I even sought help from Stack Exchange to learn the method. The method you gave is much simpler and straight forward, and I wish I had thought to go in that direction. 3) The second half of the Kreweras paper applies the author's result to political gerrymandering(!)
Edited on November 8, 2023, 10:06 pm
thanks
