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

1,2

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

Table of n, a(n) for n=1..12.

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.

Sequence in context: A362259 A120599 A012797 * A358544 A167002 A227005

Adjacent sequences: A342904 A342905 A342906 * A342908 A342909 A342910

Keyword

nonn,more

Author

N. J. A. Sloane, Mar 31 2021

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

Status

approved