[seqfan] Re: Toothpick A139250 defines set of graphs.

Richard Mathar mathar at strw.leidenuniv.nl
Wed Jan 13 12:56:27 CET 2010

Omar points out that the number of faces in the toothpick graph A139250
that I computed in
are already in A160124, plus the corresponding differences A160125.

The definition A160124 "Total number of squares and rectangles..." might
(i) be misunderstood to count also overlapping cases, that is tiles of adjacent
squares and rectangles glued to tiles to larger size. This here is a total
of 3 squares and rectangles:
    | |
    | |
The upper one, the lower one, and the covering (united) one.

(ii) vague in the sense that it does not say whether squares and rectangles
have all perimeters closed by toothpicks. This here is a square defined
by three toothpicks, although the left side is open (not covered):

In that sense, a definition in A160124 like "Number of non-overlapping
rectangles in A139250 (faces of the associated graph)" might be better.
I assume that squares are rectangles; mentioning both is redundant.

Richard Mathar

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