A367528 The number of ways of tiling the n X n grid up to diagonal and antidiagonal reflections by a tile that is fixed under 180-degree rotations but is not fixed under either reflection.

1, 5, 136, 16448, 8390656, 17179934720, 140737496743936, 4611686019501129728, 604462909807864343166976, 316912650057057631849152512000, 664613997892457937028364282443595776, 5575186299632655785385110159782807787798528, 187072209578355573530071668259090783432992763150336

Offset

1,2

Links

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

Peter Kagey, Illustration of a(2)=5

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) = 2^(2m^2 - 4m - 1)*(4^m + 4^m^2).

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

Mathematica

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

Crossrefs

Cf. A367524, A367526, A367527, A367529.

Sequence in context: A082212 A208867 A094808 * A320995 A061453 A215958

Adjacent sequences: A367525 A367526 A367527 * A367529 A367530 A367531

Keyword

nonn

Author

Peter Kagey, Dec 10 2023

Status

approved