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

Author

Peter Kagey, Dec 11 2023

Keywords

• nonn

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.

Crossrefs

Cf. A047937, A367525, A367529, A367531.

Programs

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).