A342907 a(n) is the number of tilings of the order-n Aztec Diamond by square tetrominoes and Z-shaped tetrominoes, counting all rotations and reflections as distinct.

1, 4, 20, 304, 6784, 407684, 39072966, 9449433606, 3830070645700, 3762885306351756, 6402694828334379856, 25695884677997378383120

Offset: 1

Author

N. J. A. Sloane, Mar 31 2021

Keywords

• nonn
• more

Comments

Computed by Don Reble, Mar 31 2021; a(8) from Mike Beeler, Mar 31 2021; a(9) from Walter Trump, Apr 01 2021

Comments from Allan C. Wechsler, Mar 31 2021: (Start)

Motivated by a query from James Propp in the Math-Fun forum, Mar 28 2021.

An Aztec Diamond of order n is a set of squares whose centers are at distance n or closer to a vertex in the taxicab metric.

Tilings by dominoes are counted by A006125. (End)

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.

Crossrefs

Cf. A006125.

Extensions

a(10) from Andrew Howroyd, Apr 01 2021

a(11) from Walter Trump, Apr 06 2021

a(12) from Bert Dobbelaere, May 21 2021