A356512 a(n) is the number of tilings of the Aztec diamond of order n using dominoes and square tetrominoes.

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

Table of n, a(n) for n=0..12.

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: A338772 A231620 A268646 * A143597 A224681 A115705

Adjacent sequences: A356509 A356510 A356511 * A356513 A356514 A356515

Keyword

nonn

Author

James Propp, Aug 09 2022

Status

approved