[seqfan] Re: Bad pdf file in A002369?

Richard J. Mathar mathar at mpia-hd.mpg.de
Sun Feb 25 21:00:45 CET 2018


Picking up an idea of http://list.seqfan.eu/pipermail/seqfan/2018-February/018364.html:
Supposed we map rectangular polyomino shapes of A056780 onto trees, where
stepping from one rectangle to a neighbour is an edge of the tree, and where
shapes are discarded if that cannot be done uniquely (e.g. because there are
2x2 or larger blocks, non-tatami blocks, which do not have a unique direction
of traversal.) Then label each edge of the tree with either "s" if it means
passing through a short edge, or with "l" if it means passing through a long
edge. 
This will end in the number of (unrooted) trees with bicolored edges, node
degrees <=4 (somehwere in the OEIS?) and it will map some of the distinct
shapes of A056780 onto the same tree, because some of the north-south-east-west
information of the steps is lost.

Then in A056780 for (n=4) the shape

XX
XX

does not count and we're down to 8. In A05670 for (n=5) the shapes

XX
XXX

X
XX
XX

do not count and

X X
XXX

is the same as 

  X
XXX
X

so we're down from 21 to 18.


Does this come closer to explain A002369?

RJM


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