A367526 The number of ways of tiling the n X n grid up to diagonal and antidiagonal reflections by two tiles that are each fixed under both of these reflections.
2, 9, 168, 16960, 8407040, 17180983296, 140737630961664, 4611686053860868096, 604462909825456529211392, 316912650057075646247661993984, 664613997892457973921852429862699008, 5575186299632655785536225887234636434636800, 187072209578355573530072906199130068813267662274560
Offset: 1
Keywords
Links
- Peter Kagey, Illustration of a(2)=9
- 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.
Programs
-
Mathematica
Table[{2^(2 m^2 - 4 m - 1) (4^m + 4^m^2 + 8^m), 4^(m^2 - 1) (1 + 2^(1 + m) + 4^m^2)}, {m, 1, 5}] // Flatten
Formula
a(2m-1) = 2^(2m^2 - 4m - 1)(4^m + 4^m^2 + 8^m).
a(2m) = 4^(m^2 - 1)(1 + 2^(1 + m) + 4^m^2).