A367531 The number of ways of tiling the n X n grid up to 90-degree rotation by a tile that is fixed under 180-degree rotation but not 90-degree rotation.

1, 6, 136, 16456, 8390656, 17179934976, 140737496743936, 4611686019501162496, 604462909807864343166976, 316912650057057631849169289216, 664613997892457937028364282443595776, 5575186299632655785385110159782842147536896, 187072209578355573530071668259090783432992763150336

Offset

1,2

Links

Table of n, a(n) for n=1..13.

Peter Kagey, Illustration of a(3)=136

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.

Formula

a(2*n-1) = 2^(2n^2 - 4n - 1)*(4^n + 4^n^2).

a(2*n) = 2^(n^2 - 2)*(2 + 2^n^2 + 8^n^2).

Mathematica

Table[{2^(2 m^2 - 4 m - 1)*(4^m + 4^m^2), 2^(m^2 - 2)*(2 + 2^m^2 + 8^m^2)}, {m, 1, 5}] // Flatten

Crossrefs

Cf. A047937, A367532.

Sequence in context: A196946 A090407 A222915 * A245104 A075185 A376113

Adjacent sequences: A367528 A367529 A367530 * A367532 A367533 A367534

Keyword

nonn

Author

Peter Kagey, Dec 11 2023

Status

approved