%I #13 Apr 29 2023 08:10:57
%S 1,1,2,10,116,3212,209152,32133552,11631456480,9922509270288,
%T 19946786274879008,94492874103638971552,1054865198752147761744448
%N a(n) is the number of tilings of the Aztec diamond of order n using horizontal skew tetrominoes, horizontal straight tetrominoes, and square tetrominoes.
%C It appears that a(n) is divisible by 2^floor(n/2).
%H James Propp, <a href="https://arxiv.org/abs/2204.00158">Some 2-adic conjectures concerning polyomino tilings of Aztec diamonds</a>, arXiv:2204.00158 [math.CO], 2022, section 6. See also <a href="https://doi.org/10.5281/zenodo.7859005">Integers</a> (2023) Vol. 23, Art. A30.
%e 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).
%K nonn
%O 0,3
%A _James Propp_, Aug 09 2022