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

1,1

Links

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

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.

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).

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

Crossrefs

Cf. A054247, A367526, A367527, A367528, A367529.

Sequence in context: A081459 A336213 A038843 * A237201 A053294 A199695

Adjacent sequences: A367523 A367524 A367525 * A367527 A367528 A367529

Keyword

nonn

Author

Peter Kagey, Dec 10 2023

Status

approved