[seqfan] Re: Polyomino miscellany

[Neil Sloane]

A126202 is part of a collection of sequences that counted various "things"
with a distinguished element.
The a(0)=1 was a convention that seemed natural for the whole collection -
in line with the convention
that the number of partitions of 0 is 1 (because of the generating
function, mostly).
It was just a convention, but there was a reason for it.

Best regards
Neil

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



On Thu, Dec 27, 2018 at 2:29 AM Alex Meiburg <timeroot.alex at gmail.com>
wrote:

> Hmm, I'd agree, on the basis that zero-choose-one is either zero or
> undefined.
>
> On Wed, Dec 26, 2018, 11:03 PM Allan Wechsler <acwacw at gmail.com wrote:
>
> > Earlier I posted about my misadventures trying to write a Haskell program
> > to compute A048664, which counts oriented polyominoes with a particular
> > cell chosen as the "origin". Rotations, reflections, and different
> choices
> > of the origin cell are all considered different.
> >
> > I had a bug in my program, which produced a sequence that grew quite a
> bit
> > faster than A048664 -- the first discrepancy was that a(3) was 24 instead
> > of 18.
> >
> > I found the bug, and now know what I was counting, and the concept seems
> > interesting enough to add to OEIS, so I will probably do that in a few
> > days. For the moment I'm going to keep my explanation secret, in case
> > anyone wants to have fun figuring out the "secret rule" (knowing that it
> > arose from a buggy polyomino-counter).
> >
> > (I fixed the bug, as well, and the program now produces A048664 just fine
> > -- except that it in excruciatingly slow.)
> >
> > While fossicking among the polyomino sequences, I noticed A126202, which
> > also counts polyominoes with a single distinguished cell, but this
> sequence
> > regards rotations and reflections as equivalences. I was intrigued to
> note
> > that, unlike the extremely similar A048664, A126202 has an offset of 0;
> it
> > says there is one pointed nullomino.
> >
> > Now, I am an enthusiastic supporter of the Zero Liberation Front. Zero
> is a
> > good number, the empty set is a a good set, and the nullomino is a good
> > polyomino, and should be counted wherever this can be remotely justified.
> > But I cannot see the justification for counting it (more than zero times)
> > in the case of A126202. The problem is that it has no cells from among
> > which to select the "origin". There is a nullomino, yes -- but there is
> no
> > nullomino with exactly one distinguished cell. In this case, I think
> > A048664 (which is 1-offset) got it right. If a(0) must be defined in
> either
> > case, I think, the only defensible value is 0, because there are no
> objects
> > satisfying the definition. Can anyone defend A126202(0) = 1?
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
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