tiling a 2xn checkerboard with square tetrominoes and dominoes

[Jonathan Post]

Yes, thank you,  Tanya Khovanova.  I realized that a few minutes
later, as  Joshua Zucker and I emailed each other offline.  We
eventually converged (with his doing most of the correcting of my
mistakes) and we arrived at what shall be submitted as a comment on
A001045.

Now we're working on 3xn boards tiled with 1x2 dominoes, 2x2 square
tetrominoes, and 3x3 square nonominoes. Again, he and I, offline,
partly agree and partly disagree though 3x8,  and are debugging each
other.  He's usually right.

It was kind of you to point out my missing the easiest case in that
example. Would that politicians and corporate managers were also
trained to appreciate being corrected!

Happy Year of the Boar,

Jonathan Vos Post