OEIS sequence request thread

[PHPBB12345]

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# The number of unique transitions for n-dimensional Moore isotropic non-totalistic rulespaces:
0 1
1 3
2 51
3 1426144
4 3148244699232062849152

[confocaloid]

Maybe someone could double-check and extend the following:

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1 polyplets of size 1, 1 patterns with MCPS <= 1, 1 patterns with MCPS = 1
2 polyplets of size 2, 3 patterns with MCPS <= 2, 2 patterns with MCPS = 2
5 polyplets of size 3, 11 patterns with MCPS <= 3, 8 patterns with MCPS = 3
22 polyplets of size 4, 50 patterns with MCPS <= 4, 39 patterns with MCPS = 4
94 polyplets of size 5, 285 patterns with MCPS <= 5, 235 patterns with MCPS = 5
524 polyplets of size 6, 1939 patterns with MCPS <= 6, 1654 patterns with MCPS = 6
3031 polyplets of size 7, 14605 patterns with MCPS <= 7, 12666 patterns with MCPS = 7
18770 polyplets of size 8, 115597 patterns with MCPS <= 8, 100992 patterns with MCPS = 8

The first column is the number of polyplets with n cells; it agrees with OEIS A030222 up to n = 8. Second and third columns seem to agree with previous manual enumeration (see quote below) up to n = 4. I did not continue past n = 8 as the Python script I used for this is extremely inefficient.

Edit: I got the following line for n = 9:

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118133 polyplets of size 9, 938666 patterns with MCPS <= 9, 823069 patterns with MCPS = 9

(...)

[confocaloid]

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The number of different orientations of n-bit strict still lives in B3/S23,
with respect to a glider arriving from a fixed direction.
(E.g. the loaf has three distinct orientations.)
 4   2
 5   3
 6   9
 7  12
 8  24
 9  32
10  82
11 168
12 430
...