A367532 The number of ways of tiling the n X n grid up to 90-degree rotation by a tile that is not fixed under 180-degree rotation.
1, 70, 65536, 1073758336, 281474976710656, 1180591620734591303680, 79228162514264337593543950336, 85070591730234615870455337878516924416, 1461501637330902918203684832716283019655932542976, 401734511064747568885490523085607563280607806359022338048000
Offset: 1
Keywords
Links
- Peter Kagey, Illustration of a(2)=70
- 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-10.
Programs
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Mathematica
Table[{256^(m^2 - m), 4^(m^2 - 1)*(2 + 4^m^2 + 64^m^2)}, {m, 1, 5}] // Flatten
Formula
a(2*n-1) = 256^(n^2 - n).
a(2*n) = 4^(n^2 - 1)*(2 + 4^n^2 + 64^n^2).