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

Author

Walter Trump, Apr 21 2021

Keywords

• nonn

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

• 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.