A356514 a(n) is the number of tilings of the Aztec diamond of order n using horizontal skew tetrominoes, horizontal straight tetrominoes, and square tetrominoes.

1, 1, 2, 10, 116, 3212, 209152, 32133552, 11631456480, 9922509270288, 19946786274879008, 94492874103638971552, 1054865198752147761744448

Offset

0,3

Comments

It appears that a(n) is divisible by 2^floor(n/2).

Links

Table of n, a(n) for n=0..12.

James Propp, Some 2-adic conjectures concerning polyomino tilings of Aztec diamonds, arXiv:2204.00158 [math.CO], 2022, section 6. See also Integers (2023) Vol. 23, Art. A30.

Example

For n=2 there are just a(2)=2 tilings: one with the square at the far right and one with the square at the far left (in either case, the remainder of the Aztec diamond can be covered by skew tetrominoes in a unique way).

Crossrefs

Sequence in context: A131811 A261496 A347014 * A006121 A110951 A172477

Adjacent sequences: A356511 A356512 A356513 * A356515 A356516 A356517

Keyword

nonn

Author

James Propp, Aug 09 2022

Status

approved