[seqfan] Dissecting a square into squares, unfinished business

Neil Sloane njasloane at gmail.com
Sat Apr 13 05:36:31 CEST 2013


Dear Seq Fans, Early this morning Paola Lava pointed out that there were
two versions of A034295 in the OEIS. I merged them and now there is only
one.

But this looks at how many ways there are to dissect a square into squares,
KEEPING TRACK ONLY OF THE NUMBERS OF PARTS OF EACH SIZE, and ignoring the
geometry.

On the other hand, A045846 gives the number of ways when you do
look at the geometry. E.g. a(3) = 6: you can have a 3x3 square, or nine 1x1
squares, or one 2x2 square and 5 1x1 squares where the 2x2 square can be in
any of the 4 corners: total is A045846(3)=6.

But if we take the latter sequence and say that two
dissections are equivalent if a rotation/reflection takes one into the
other,
the number of inequivalent dissections is (for n=1,2,3,4)
1,2,3,13
and I think this sequence is missing from the the OEIS.

I can send anyone who is interested a drawing of the first 4 terms
(we are not allowed attachments on this mailing list).

How does it continue?

Neil

-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


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