A356513 a(n) is the number of tilings of the Aztec diamond of order n using horizontal skew tetrominoes and square tetrominoes.

1, 1, 2, 6, 40, 364, 7904, 226152, 15835008, 1439900880, 324189571584, 94080051207136, 68041472016287744, 63145927127133361600, 146637148542938673930240, 435697213021432661980535936

Offset

0,3

Comments

It appears that for n, the multiplicity of 2 in the prime factorization of a(n) is n-1 if n is even and (n-1)/2 if n is odd.

Links

Table of n, a(n) for n=0..15.

James Propp, Some 2-adic conjectures concerning polyomino tilings of Aztec diamonds, arXiv:2204.00158 [math.CO], 2022, section 4. 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: A267981 A343846 A318006 * A292407 A274275 A081471

Adjacent sequences: A356510 A356511 A356512 * A356514 A356515 A356516

Keyword

nonn

Author

James Propp, Aug 09 2022

Status

approved