[seqfan] Re: Bad pdf file in A002369?

Joseph Myers jsm at polyomino.org.uk
Sun Feb 25 00:57:31 CET 2018


On Sat, 24 Feb 2018, Richard J. Mathar wrote:

> The construction of sequence A002369 is not clear to me either
> (probably because I don't understand the fine-tuned French).
> A056780 counts the shapes of polyominoes of rectangular cells, where 
> polyominoes are considered equivalent if they can be
> mapped onto each other by the symmetry group of the
> rectangle of order 4 (unity, 180 degrees rotations, horizontal flip,
> vertical flip). 
> Devisme seems to say he has counted A002369 by counting a tree-structure
> and by considering paths stepping across connected cells horizontally
> or vertically.
> So which shapes of A056780 are not counted in A002369 and why?

If it's specifically meant to be strips of stamps, one might suppose that 
some internal edges of the polyomino are to be severed so that the graph 
of the result is a path.  This would result in two variants of the square 
tetromino instead of one, but both variants of the T tetromino would be 
removed, so resulting in the count of 8.  Unfortunately, that (which if 
you start with squares rather than rectangles would be A037245 with an 
additional leading term of 1) doesn't agree with all the other figures.  
I get: 1, 2, 3, 8, 16, 44, 106, 294, 762, 2094, 5572, 15200, 40778, 
110626, 297236, 803258, 2156828, 5811502.

-- 
Joseph S. Myers
jsm at polyomino.org.uk


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