tiling a 2xn checkerboard with square tetrominoes and dominoes

[Jonathan Post]

Whoops.  I found the 1 I missed for 2x4 (2 tetrominoes, the easy
case), so I'm wrong, you're right, a(2x4) = 11.

I found the ones I missed for 2x6, so yoiu're right again: a(2x6) =
43.  We agree on the a(2x7) = 85.

So much for careless hand-drawings on my part.  Which is why I asked
seqfans, and you leapt bravely into the breach.

I stand corrected.  So the formula, and extension is?



Hello seqfans,

I've found two sequences in the book by I.M.Yaglom "How to dissect a square" (In Russian). The first sequence is the number of different tilings of a rectangle into n squares:
2, 10, 38, 127, 408 (Starting from n = 9).
The other one is the number of different SIMPLE tilings of a rectangle into n squares:
2, 6, 22, 67, 213.
The second sequence is in the OEIS: A002839 Number of perfect squared rectangles of order n. 
But the first one is not in OEIS. 

Yaglom refers to Bouwkamp papers (and I can't access them).

I do not want to submit the sequence personally as I do not know English terminology for this subject and I have no way to check that this is correct. At the same time I think that this sequence should be in OEIS.

Can someone check it and submit it?

Tanya




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