A364504 Number of tilings of an n X n square using dominoes and trominoes (of any shape).

1, 0, 2, 30, 1352, 226922, 128441094, 267855152858, 1990875917805852, 52918918728713551244, 5046393600526600826576990, 1722423352379200292770200349728, 2106175531602971710801901685263906946, 9224774497259881798661234516031754156588512, 144713995908210595144464778124853904625705818728754

Offset

0,3

Links

David Radcliffe, Table of n, a(n) for n = 0..17 (computed by Liang Kai).

Liang Kai, Solving tiling enumeration problems by tensor network contractions, arXiv:2503.17698 [math.CO], 2025.

Liang Kai, Tiling, GitHub repository.

Wikipedia, Domino (mathematics)

Wikipedia, Tromino

Formula

a(n) = A364457(n,n).

Crossrefs

Main diagonal of A364457.

Cf. A219874, A219994.

Sequence in context: A246741 A089016 A262004 * A132104 A208093 A144501

Adjacent sequences: A364501 A364502 A364503 * A364505 A364506 A364507

Keyword

nonn

Author

Alois P. Heinz, Jul 26 2023

Extensions

Terms n>=4 had to be corrected as was pointed out by Martin Fuller and David Radcliffe - Alois P. Heinz, Apr 05 2025

a(13)-a(17) from David Radcliffe, Apr 07 2025

Status

approved