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%I #16 Apr 29 2023 08:11:05
%S 1,3,19,293,10917,996599,222222039,121552500713,162860556763865,
%T 535527565429290907,4318205059450240425083,85475498697714319842817853,
%U 4151186175463797888945512144221
%N a(n) is the number of tilings of the Aztec diamond of order n using dominoes and square tetrominoes.
%C It appears that for all k, the mod 2^k residue of a(n) is periodic with period dividing 2^k.
%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 3. See also <a href="https://doi.org/10.5281/zenodo.7859005">Integers</a> (2023) Vol. 23, Art. A30.
%e For n=1 the 3 tilings use 2 horizontal dominoes, 2 vertical dominoes, and 1 square tetromino, respectively.
%K nonn
%O 0,2
%A _James Propp_, Aug 09 2022
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