A226979
Number of ways to cut an n X n square into squares with integer sides, reduced for symmetry, where the orbits under the symmetry group of the square, D4, have 2 elements.
Original entry on oeis.org
0, 0, 0, 2, 2, 24, 36, 344, 504, 7657, 11978, 289829
Offset: 1
For n=5, there are 2 dissections where the orbits under the symmetry group of the square, D4, have 2 elements.
For n=4, the 2 dissections can be seen in A240120 and A240121.
a(8)-a(12) from
Ed Wynn, Apr 01 2014
A240120
Number of inequivalent ways to cut an n X n square into squares with integer sides, such that the dissection has reflective symmetry in both diagonals and no other reflective symmetries.
Original entry on oeis.org
0, 0, 0, 1, 1, 9, 19, 121, 275, 2489, 7217, 86775
Offset: 1
This is the single dissection for n=4:
---------
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| -----
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---------
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----- |
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---------
A240122
Number of inequivalent ways to cut an n X n square into squares with integer sides, such that the dissection has 90-degree rotational symmetry and no reflective symmetry.
Original entry on oeis.org
0, 0, 0, 0, 1, 2, 12, 40, 154, 760, 3260, 22730
Offset: 1
The two dissections for n=6:
------------- -------------
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--- ------- --- -------
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--------- | --------- |
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----- ----- -------------
| | | | | | | | | | |
| --------- ---------
| | | | | | | | | |
------- --- ------- ---
| | | | | | | | | | | |
------------- -------------
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