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A356523 a(n) is the number of tilings of the Aztec diamond of order n using dominoes and horizontal straight tetrominoes. 1
1, 2, 11, 209, 12748, 2432209, 1473519065, 2827837404882, 17158790773744279, 329479797284568074621, 20021122370390985464701796, 3849702362426399132776261664897, 2342395734889640880082957470488832361 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
It appears that a(n) is even when n is congruent to 1 (mod 3) and is odd otherwise.
LINKS
James Propp, Some 2-adic conjectures concerning polyomino tilings of Aztec diamonds, arXiv:2204.00158 [math.CO], 2022, section 5. See also Integers (2023) Vol. 23, Art. A30.
EXAMPLE
For n=2 there are 8 ways to tile using just dominoes, and 3 ways to tile using one or more horizontal straight tetrominoes (in the second row, third row, or both), for a total of 11 tilings.
CROSSREFS
Sequence in context: A358649 A188203 A070256 * A020450 A036229 A104337
KEYWORD
nonn
AUTHOR
James Propp, Aug 10 2022
STATUS
approved

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Last modified July 22 00:58 EDT 2024. Contains 374478 sequences. (Running on oeis4.)