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

1,2

Links

Table of n, a(n) for n=1..10.

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.

Formula

a(2m-1) = 256^(m^2 - m).

a(2m) = 1/4 (16^m^2 + 256^m^2).

Mathematica

Table[{256^(m^2 - m), 1/4*(16^m^2 + 256^m^2)}, {m, 1, 5}] // Flatten

Crossrefs

Cf. A367525, A367526, A367527, A367528.

Sequence in context: A177666 A292607 A211311 * A203757 A159385 A116196

Adjacent sequences: A367526 A367527 A367528 * A367530 A367531 A367532

Keyword

nonn

Author

Peter Kagey, Dec 10 2023

Status

approved