A123819
Number of ways, counted up to symmetry, to build a contiguous building with n LEGO blocks of size 2 X 2 which is symmetric after a rotation by 180 degrees.
Original entry on oeis.org
1, 1, 5, 8, 65, 126, 1023, 2187, 17585, 39606, 315326, 737302
Offset: 1
A123820
Number of ways, counted up to symmetry, to build a contiguous building with n LEGO blocks of size 2 X 2 which is symmetric after a rotation by 90 degrees.
Original entry on oeis.org
1, 1, 1, 1, 3, 4, 5, 10, 26, 38, 51, 121, 324, 488, 673, 1808
Offset: 1
A123821
Number of ways to build a contiguous building with n LEGO blocks of size 2 X 2 on top of a fixed block of the same size.
Original entry on oeis.org
9, 97, 1349, 20288, 329707, 5574248, 97506021, 1747201171, 31923371982, 592403479154
Offset: 1
A123822
Number of ways to build a contiguous building with n LEGO blocks of size 2 X 2 on top of a fixed block of the same size so that the building is symmetric after a rotation by 180 degrees.
Original entry on oeis.org
1, 5, 9, 44, 111, 576, 1541, 8199, 23750, 127654, 384817, 2083235
Offset: 1
A123823
Number of ways to build a contiguous building with n LEGO blocks of size 2 X 2 on top of a fixed block of the same size so that the building is symmetric after a rotation by 90 degrees.
Original entry on oeis.org
1, 1, 1, 2, 3, 4, 5, 11, 22, 34, 47, 113
Offset: 1
A123825
Number of ways, counted up to symmetry, to build a contiguous building with n LEGO blocks of size 2 X 3 which is symmetric after a rotation by 180 degrees.
Original entry on oeis.org
1, 1, 25, 53, 1189, 2947, 66094, 181955, 3979943
Offset: 1
A123826
Number of ways to build a contiguous building with n LEGO blocks of size 2 X 3 on top of a fixed block of the same size.
Original entry on oeis.org
31, 1165, 57415, 3060464, 176633912, 10625603236, 661642082820
Offset: 1
A123830
Number of ways to build a contiguous building with n LEGO blocks of size 2 X 4 on top of a fixed block of the same size.
Original entry on oeis.org
46, 2596, 194834, 15834801, 1395436949, 128352319891, 12224079725173, 1193967045643245, 118973723976420310
Offset: 1
From _Matthias Simon_, Aug 16 2018: (Start)
Explanation to a(1): There is a 2 X 4 LEGO block fixed at the ground. There are 46 ways to put a building consisting of n=1 LEGO block onto the fixed block, because:
1) For n=1, the figure is just another LEGO block.
2) If the two LEGO blocks are parallel, the upper LEGO block can be shifted in 3*7 = 21 different ways relatively to the lower one.
3) If the LEGO blocks are in a right angle to each other, the upper LEGO block can be shifted in 5*5 = 25 different ways relatively to the lower one.
4) Summing up: a(1) = 21 + 25 = 46.
Explanations to a(2): Two additional LEGO blocks are added to a fixed one. The first additional block is put onto the fixed one, the second additional block ...
a) ... may also be put onto the fixed block (if there are free studs)
b) ... or may be put onto the first additional block.
Following a), 480 figures can be obtained.
Following b), 46^2 = 2116 figures can be obtained.
Summing up: a(2) = 480 + 2116 = 2596.
(End)
A123831
Number of ways to build a contiguous building with n LEGO blocks of size 2 X 4 on top of a fixed block of the same size so that the building is symmetric after a rotation by 180 degrees.
Original entry on oeis.org
2, 24, 88, 1079, 5563, 74597, 412309, 5633649
Offset: 1
A123837
Number of ways to build a contiguous building with n LEGO blocks of size 3 X 3 on top of a fixed block of the same size so that the building is symmetric after a rotation by 90 degrees.
Original entry on oeis.org
1, 1, 1, 4, 7, 10, 13, 61, 154, 256
Offset: 1
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