A226980
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 4 elements.
Original entry on oeis.org
0, 0, 1, 6, 26, 264, 1157, 23460, 153485, 6748424, 70521609, 6791578258
Offset: 1
For n=5, there are 26 dissections where the orbits under the symmetry group of the square, D4, have 4 elements.
The 6 dissections for n=4 can be seen in A240123 and A240125.
a(8)-a(12) from
Ed Wynn, Apr 01 2014
A240124
Number of inequivalent ways to cut an n X n square into squares with integer sides, such that the dissection has 180-degree rotational symmetry, but no other symmetries.
Original entry on oeis.org
0, 0, 0, 0, 2, 19, 109, 1781, 13660, 397689, 5368943, 289864745
Offset: 1
The two dissections for n=5:
----------- -----------
| | | | | | | | |
| | --- --- -----
| | | | | | | | |
----------- -----------
| | | | | | | | | | | |
----------- -----------
| | | | | | | | |
--- | | ----- ---
| | | | | | | | |
----------- -----------
A240125
Number of inequivalent ways to cut an n X n square into squares with integer sides, such that the dissection has one reflective symmetry in an axis parallel to a side, but no other symmetries.
Original entry on oeis.org
0, 0, 0, 3, 5, 138, 201, 13032, 19990, 4095612, 7026883, 4451051502
Offset: 1
The three dissections for n=4, with the axis horizontal:
--------- --------- ---------
| | | | | | | | | | | | |
| ----- | ----- ---------
| | | | | | | | | | |
--------- ----- | | -----
| | | | | | | | | | |
| ----- | ----- ---------
| | | | | | | | | | | | |
--------- --------- ---------
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