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interests / rec.puzzles / Number of free polyominoes (or square animals) with n cells.

SubjectAuthor
* Number of free polyominoes (or square animals) with n cells.henh...@gmail.com
`* Re: Number of free polyominoes (or square animals) with n cells.Edward Murphy
 `* Re: Number of free polyominoes (or square animals) with n cells.henh...@gmail.com
  `- Re: Number of free polyominoes (or square animals) with n cells.henh...@gmail.com

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Number of free polyominoes (or square animals) with n cells.

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Subject: Number of free polyominoes (or square animals) with n cells.
From: henha...@gmail.com (henh...@gmail.com)
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 by: henh...@gmail.com - Sun, 30 Oct 2022 01:54 UTC

we're (were) counting rotation, reflection as Separate Animals.
so our seq. went:
1, 2, 6, 19, ..............

---------- is this seq. not in oeis ?

(we say 19, the following list says 5)

https://oeis.org/A000105

A000105 Number of free polyominoes (or square animals) with n cells.
(Formerly M1425 N0561)

1, 1, 1, 2, 5, 12, 35, 108, 369, 1285, 4655, 17073, 63600, 238591, 901971, 3426576, 13079255, 50107909, 192622052, 742624232, 2870671950, 11123060678, 43191857688, 168047007728, 654999700403, 2557227044764, 9999088822075, 39153010938487, 153511100594603

( starts with 0-cell animal )

Re: Number of free polyominoes (or square animals) with n cells.

<tjkqoc$1tiu$1@gioia.aioe.org>

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From: emurph...@zoho.com (Edward Murphy)
Newsgroups: rec.puzzles
Subject: Re: Number of free polyominoes (or square animals) with n cells.
Date: Sat, 29 Oct 2022 20:23:56 -0700
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 by: Edward Murphy - Sun, 30 Oct 2022 03:23 UTC

On 10/29/2022 6:54 PM, henh...@gmail.com wrote:

> we're (were) counting rotation, reflection as Separate Animals.
> so our seq. went:
> 1, 2, 6, 19, ..............
>
> ---------- is this seq. not in oeis ?
>
>
> (we say 19, the following list says 5)
>
>
>
>
> https://oeis.org/A000105
>
> A000105 Number of free polyominoes (or square animals) with n cells.
> (Formerly M1425 N0561)
>
> 1, 1, 1, 2, 5, 12, 35, 108, 369, 1285, 4655, 17073, 63600, 238591, 901971, 3426576, 13079255, 50107909, 192622052, 742624232, 2870671950, 11123060678, 43191857688, 168047007728, 654999700403, 2557227044764, 9999088822075, 39153010938487, 153511100594603
>
>
> ( starts with 0-cell animal )

https://oeis.org/A001168

A001168 Number of fixed polyominoes with n cells.
(Formerly M1639 N0641) 52
1, 1, 2, 6, 19, 63, 216, 760, 2725, 9910, 36446, 135268, 505861,
1903890, 7204874, 27394666, 104592937, 400795844, 1540820542,
5940738676, 22964779660, 88983512783, 345532572678, 1344372335524,
5239988770268, 20457802016011, 79992676367108, 313224032098244,
1228088671826973

Re: Number of free polyominoes (or square animals) with n cells.

<e8e3f102-2d46-40ed-bd94-4be29c8c48dan@googlegroups.com>

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Subject: Re: Number of free polyominoes (or square animals) with n cells.
From: henha...@gmail.com (henh...@gmail.com)
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 by: henh...@gmail.com - Sun, 30 Oct 2022 03:29 UTC

On Saturday, October 29, 2022 at 8:23:59 PM UTC-7, Edward Murphy wrote:
> On 10/29/2022 6:54 PM, henh...@gmail.com wrote:
>
> > we're (were) counting rotation, reflection as Separate Animals.
> > so our seq. went:
> > 1, 2, 6, 19, ..............
> >
> > ---------- is this seq. not in oeis ?
> >
> >
> > (we say 19, the following list says 5)
> >
> >
> >
> >
> > https://oeis.org/A000105
> >
> > A000105 Number of free polyominoes (or square animals) with n cells.
> > (Formerly M1425 N0561)
> >
> > 1, 1, 1, 2, 5, 12, 35, 108, 369, 1285, 4655, 17073, 63600, 238591, 901971, 3426576, 13079255, 50107909, 192622052, 742624232, 2870671950, 11123060678, 43191857688, 168047007728, 654999700403, 2557227044764, 9999088822075, 39153010938487, 153511100594603
> >
> >
> > ( starts with 0-cell animal )

> https://oeis.org/A001168
>
> A001168 Number of fixed polyominoes with n cells.
> (Formerly M1639 N0641) 52
> 1, 1, 2, 6, 19, 63, 216, 760, 2725, 9910, 36446, 135268, 505861,
> 1903890, 7204874, 27394666, 104592937, 400795844, 1540820542,
> 5940738676, 22964779660, 88983512783, 345532572678, 1344372335524,
> 5239988770268, 20457802016011, 79992676367108, 313224032098244,
> 1228088671826973

thank you... i think there are 2 more variations (in between)

--- allows rotation only

--- allows reflection only

M.Gardner's [The Colosal Book of Math.] has some stuff on Pentominoes (3-D)

Re: Number of free polyominoes (or square animals) with n cells.

<2019c0c7-1a8a-47d6-b36c-7369cad1b7d4n@googlegroups.com>

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<tjkqoc$1tiu$1@gioia.aioe.org> <e8e3f102-2d46-40ed-bd94-4be29c8c48dan@googlegroups.com>
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Subject: Re: Number of free polyominoes (or square animals) with n cells.
From: henha...@gmail.com (henh...@gmail.com)
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 by: henh...@gmail.com - Tue, 1 Nov 2022 18:55 UTC

On Saturday, October 29, 2022 at 8:29:53 PM UTC-7, henh...@gmail.com wrote:
> On Saturday, October 29, 2022 at 8:23:59 PM UTC-7, Edward Murphy wrote:
> > On 10/29/2022 6:54 PM, henh...@gmail.com wrote:
> >
> > > we're (were) counting rotation, reflection as Separate Animals.
> > > so our seq. went:
> > > 1, 2, 6, 19, ..............
> > >
> > > ---------- is this seq. not in oeis ?
> > >
> > >
> > > (we say 19, the following list says 5)
> > >
> > >
> > >
> > >
> > > https://oeis.org/A000105
> > >
> > > A000105 Number of free polyominoes (or square animals) with n cells.
> > > (Formerly M1425 N0561)
> > >
> > > 1, 1, 1, 2, 5, 12, 35, 108, 369, 1285, 4655, 17073, 63600, 238591, 901971, 3426576, 13079255, 50107909, 192622052, 742624232, 2870671950, 11123060678, 43191857688, 168047007728, 654999700403, 2557227044764, 9999088822075, 39153010938487, 153511100594603
> > >
> > >
> > > ( starts with 0-cell animal )
>
>
> > https://oeis.org/A001168
> >
> > A001168 Number of fixed polyominoes with n cells.
> > (Formerly M1639 N0641) 52
> > 1, 1, 2, 6, 19, 63, 216, 760, 2725, 9910, 36446, 135268, 505861,
> > 1903890, 7204874, 27394666, 104592937, 400795844, 1540820542,
> > 5940738676, 22964779660, 88983512783, 345532572678, 1344372335524,
> > 5239988770268, 20457802016011, 79992676367108, 313224032098244,
> > 1228088671826973
> thank you... i think there are 2 more variations (in between)
>
> --- allows rotation only
>
> --- allows reflection only
>
>
>
> M.Gardner's [The Colossal Book of Math.] has some stuff on Pentominoes (3-D)

i think there are (at least) 2 more variations (in between 5 and 19 shapes)
--- allows Rotation only ------------------------------ 7 shapes
--- allows Horizontal Reflection only --------------------- 12 shapes
are these not in oeis ?

1
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