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A356512
a(n) is the number of tilings of the Aztec diamond of order n using dominoes and square tetrominoes.
0
1, 3, 19, 293, 10917, 996599, 222222039, 121552500713, 162860556763865, 535527565429290907, 4318205059450240425083, 85475498697714319842817853, 4151186175463797888945512144221
OFFSET
0,2
COMMENTS
It appears that for all k, the mod 2^k residue of a(n) is periodic with period dividing 2^k.
LINKS
James Propp, Some 2-adic conjectures concerning polyomino tilings of Aztec diamonds, arXiv:2204.00158 [math.CO], 2022, section 3. See also Integers (2023) Vol. 23, Art. A30.
EXAMPLE
For n=1 the 3 tilings use 2 horizontal dominoes, 2 vertical dominoes, and 1 square tetromino, respectively.
CROSSREFS
Sequence in context: A376011 A231620 A268646 * A143597 A224681 A115705
KEYWORD
nonn
AUTHOR
James Propp, Aug 09 2022
STATUS
approved