A356523 a(n) is the number of tilings of the Aztec diamond of order n using dominoes and horizontal straight tetrominoes.

1, 2, 11, 209, 12748, 2432209, 1473519065, 2827837404882, 17158790773744279, 329479797284568074621, 20021122370390985464701796, 3849702362426399132776261664897, 2342395734889640880082957470488832361

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

Sequence in context: A358649 A188203 A070256 * A020450 A036229 A104337

Adjacent sequences: A356520 A356521 A356522 * A356524 A356525 A356526

Keyword

nonn

Author

James Propp, Aug 10 2022

Status

approved