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

From henhanna@gmail.com@21:1/5 to All on Sat Oct 29 18:54:58 2022
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 )

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• From Edward Murphy@21:1/5 to henh...@gmail.com on Sat Oct 29 20:23:56 2022
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

--- SoupGate-Win32 v1.05
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• From henhanna@gmail.com@21:1/5 to Edward Murphy on Sat Oct 29 20:29:52 2022
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)

--- SoupGate-Win32 v1.05
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• From henhanna@gmail.com@21:1/5 to henh...@gmail.com on Tue Nov 1 11:55:54 2022
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 ?

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