A343595 a(n) is the number of axially symmetric tilings of the order-n Aztec Diamond by square tetrominoes and Z-shaped tetrominoes, not counting rotations and reflections as distinct.

1, 1, 2, 7, 26, 162, 1096, 12210, 149384, 2979716, 65702176, 2347717180, 93123644320, 5962338902536, 424966024145024, 48757525297347464, 6240064849995542656, 1282987881672304949776, 294690971817685508825600, 108580010933558879525595504

Offset

1,3

Comments

No tiling is symmetric to both the x- and the y-axis.

No tiling is symmetric to an oblique symmetry axis of the diamond.

If a tiling is symmetric to the x-axis then a reflection over the y-axis is equal to a rotation by 180 degrees.

The number of tilings is 4 * a(n) if rotations are counted as distinct.

All tilings have exactly the minimum number of square tetrominoes given by ceiling(n/2).

Links

Table of n, a(n) for n=1..20.

James Propp, A Pedestrian Approach to a Method of Conway, or, A Tale of Two Cities, Mathematics Magazine, Vol. 70, No. 5 (Dec., 1997), 327-340.

Walter Trump, Axially symmetric Aztec diamond tilings

Crossrefs

Cf. A342907.

Sequence in context: A345682 A005519 A290305 * A329011 A037381 A129013

Adjacent sequences: A343592 A343593 A343594 * A343596 A343597 A343598

Keyword

nonn

Author

Walter Trump, Apr 21 2021

Status

approved