login
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.
0
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
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
KEYWORD
nonn
AUTHOR
James Propp, Aug 09 2022
STATUS
approved