A367528 The number of ways of tiling the n X n grid up to diagonal and antidiagonal reflections by a tile that is fixed under 180-degree rotations but is not fixed under either reflection.
1, 5, 136, 16448, 8390656, 17179934720, 140737496743936, 4611686019501129728, 604462909807864343166976, 316912650057057631849152512000, 664613997892457937028364282443595776, 5575186299632655785385110159782807787798528, 187072209578355573530071668259090783432992763150336
Offset: 1
Keywords
Links
- Peter Kagey, Illustration of a(2)=5
- Peter Kagey and William Keehn, Counting tilings of the n X m grid, cylinder, and torus, arXiv: 2311.13072 [math.CO], 2023. See also J. Int. Seq., (2024) Vol. 27, Art. No. 24.6.1, pp. A-6, A-9.
Programs
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Mathematica
Table[{2^(2 m^2 - 4 m - 1) (4^m + 4^m^2), (4^m^2 + 16^m^2)/4}, {m, 1, 5}] // Flatten
Formula
a(2m-1) = 2^(2m^2 - 4m - 1)*(4^m + 4^m^2).
a(2m) = (4^m^2 + 16^m^2)/4.