[seqfan] Re: Polyomino miscellany
njasloane at gmail.com
Fri Dec 28 01:56:27 CET 2018
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
It was just a convention, but there was a reason for it.
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>
> Hmm, I'd agree, on the basis that zero-choose-one is either zero or
> 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
> > of the origin cell are all considered different.
> > I had a bug in my program, which produced a sequence that grew quite a
> > 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
> > regards rotations and reflections as equivalences. I was intrigued to
> > that, unlike the extremely similar A048664, A126202 has an offset of 0;
> > 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
> > 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
> > case, I think, the only defensible value is 0, because there are no
> > satisfying the definition. Can anyone defend A126202(0) = 1?
> > --
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