A367529 The number of ways of tiling the n X n grid up to diagonal and antidiagonal reflections by a tile that is not fixed under any of these symmetries.
1, 68, 65536, 1073758208, 281474976710656, 1180591620734591172608, 79228162514264337593543950336, 85070591730234615870455337876369440768, 1461501637330902918203684832716283019655932542976, 401734511064747568885490523085607563280607805796072384626688
Offset: 1
Keywords
Links
- Peter Kagey, Illustration of a(2)=68
- 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[{256^(m^2 - m), 1/4*(16^m^2 + 256^m^2)}, {m, 1, 5}] // Flatten
Formula
a(2m-1) = 256^(m^2 - m).
a(2m) = 1/4 (16^m^2 + 256^m^2).