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, Table of n, a(n) for n = 0..16
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
KEYWORD
nonn
AUTHOR
James Propp, Aug 10 2022
STATUS
approved