[seqfan] Re: Best way to submit a bunch of snake-polycube-related sequences?

[John Mason]

Hi
Arthur's mail presents one or two terminology issues.

1. Arthur suggests that the term "strip" used in OEIS should be "snake",
and "unholey strip" should be "strip".
A quick google search seems to support this, so if we can say that these
terms are consistent with the literature, then it should be OK to make the
change.
Note however that "strip" is also used for other polyforms, e.g. A003104
strip polyhexes, A151518 strip polyiamonds.

2. During the editing of A002013, the name was changed to refer to snakes
instead of strips. But also, Ed Pegg Jr's comment was changed. So it now
says that in 2009 Ed commented "Or, number of 2-sided snake polyominoes
with n cells.". But he didn't. And Ed's link "Illustrations of polyforms
<http://demonstrations.wolfram.com/PolyformExplorer/>" talks about strips,
not snakes.
Wouldn't it be more correct to leave Ed's comment as he originally made it,
and add a note?

3. I like ouroboros. Is it already in the literature? Robert A. Russell
used "ring" in a number of sequences, e.g. A324409. It's easier to spell
too...

(Arthur - you are right about skipping the predictable zeroes :-))

john

On Tue, Dec 27, 2022 at 4:37 AM Arthur O'Dwyer <arthur.j.odwyer at gmail.com>
wrote:

> Hi SeqFans, first time poster here. (So this is also a test message to see
> if my messages go through. I'll check
> http://list.seqfan.eu/pipermail/seqfan/2022-December/thread.html tomorrow
> to find out.)
>
> I've got a whole bunch of related sequences to submit: counts of (free /
> one-sided) polyominoes in (2 / 3) dimensions with property (X / Y / X+Y).
> Some of these sequences are already in OEIS.  Most aren't.  My question is,
> what's the best approach to submit this family of sequences?
>
> Considerations might include
> - avoid duplicated effort in editing/revising/approving
> - consistency with existing OEIS style
> - searchability via the search box
> - searchability/legibility to Superseeker
>
> Re the last two bullets: I asked Superseeker to "lookup 1 6 54 416 3111
> 22898 168460 1242985 9227333 68949103 518618196", and it didn't find
> anything; does this mean "A000162 minus A038119, the count of n-celled
> chiral polycubes" would be a reasonable submission? or simply that
> Superseeker ought to be improved, and it is discouraged to submit
> "redundant" sequences like that?
>
>
> Now, on to my specific sequences...
>
> https://quuxplusone.github.io/blog/2022/12/08/polyomino-snakes/
>
> Let an "ouroboros" polyform (polyomino, polycube, whatever) be defined as a
> connected polyform where each cell has exactly two facewise neighbors.
> Let a "snake" polyform be defined as a connected polyform where two cells
> have exactly one neighbor each, and each other cell has exactly two
> neighbors.
> Let a 2D polyomino "with holes" be defined as in A000104 and A057418.
> Let a "strip" polyomino be defined as a non-ouroboros snake polyomino
> without holes.
> Let a 3D polycube "with cavities" be defined as in A357083 and A355966.
>
> I have obtained a decent number of terms in the following 14 sequences:
>
> - Free strip polyominoes: *A333313*
> - Free snake polyominoes: *A002013*
> - Free ouroboros polyominoes: 1 0 1 1 4 7 31 95 420 1682 ...
> - One-sided strip polyominoes: 1 1 2 5 10 24 52 124 282 668 ...
> - One-sided snake polyominoes: *A151514*
> - One-sided ouroboros polyominoes: 1 0 1 1 4 11 45 178 762 3309 ...
> - Free snake polycubes: 1 1 2 4 12 34 125 450 1780 ...
> - Free snake polycubes with any cavities: 4 5 24 105 485 2098 9381 40566
> ...
> - Free ouroboros polycubes: 1 1 3 11 77 606 6465 74314 ...
> - Free ouroboros polycubes with any cavities: 2 0 4 23 273 ...
> - One-sided snake polycubes: 1 1 2 5 16 54 212 827 3369 ...
> - One-sided snake polycubes with any cavities: 8 10 48 210 970 4196 ...
> - One-sided ouroboros polycubes: 1 1 3 13 122 1115 12562 ...
> - One-sided ouroboros polycubes with any cavities: 3 0 8 46 545 ...
>
> And there are several related sequences that can be defined by
> adding/subtracting these, such as:
> - Free snake-or-ouroboros polyominoes: 1 1 2 4 7 13 31 66 154 348 ...
> - Chiral snake polyominoes (*A151514 minus **A002013*): 0 0 0 1 3 7 17 40
> 95 224 532 1257 ...
> - Free snake polycubes with no cavities
> - Free snake-or-ouroboros polycubes with no cavities
> and so on and so forth.
>
> Also notice that because there are no ouroboroi with an odd number of
> cells, the ouroboros-related sequences above are really like "1 0 1 0 3 0
> 11 0 77 0 606 0 6465 0 74314 0 ..."
> I think it makes sense to eliminate those predictable zeroes, but again I
> don't know how that affects consistency and searchability of the OEIS.
>
> Thanks for your help,
> Arthur
>
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