A367527 The number of ways of tiling the n X n grid up to diagonal and antidiagonal reflections by a tile that is fixed under diagonal reflection, but not antidiagonal reflection.

1, 7, 144, 16704, 8396800, 17180459008, 140737555464192, 4611686036680998912, 604462909816110680375296, 316912650057066639048407252992, 664613997892457954898647603849723904, 5575186299632655785460668023508722111217664, 187072209578355573530072277557703869206096815063040

Offset: 1

Author

Peter Kagey, Dec 10 2023

Keywords

• nonn

Links

• Peter Kagey, Illustration of a(2)=7
• 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.

Crossrefs

Cf. A302484, A367526, A367528, A367529.

Programs

Mathematica

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

Formula

a(2m-1) = 2^(2m^2 - 4m - 2)*(2^(1 + 2 m^2) + 8^m).

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