A172477 The number of ways to dissect an n X n square into polyominoes of size n.

1, 2, 10, 117, 4006, 451206, 158753814, 187497290034, 706152947468301, 8576037567452146180

Offset

1,2

Links

Table of n, a(n) for n=1..10.

Jiahua Chen, Aneesha Manne, Rebecca Mendum, Poonam Sahoo, and Alicia Yang, Minority Voter Distributions and Partisan Gerrymandering, arXiv:1911.09792 [cs.CY], 2019.

Johan de Ruiter, On Jigsaw Sudoku Puzzles and Related Topics, Bachelor Thesis, Leiden Institute of Advanced Computer Science, 2010.

Christopher Donnay and Matthew Kahle, Asymptotics of Redistricting the n X n grid, arXiv:2311.13550 [math.CO], 2023.

R. S. Harris, Counting Nonomino Tilings and Other Things of that Ilk, G4G9 Gift Exchange book, 2010.

R. S. Harris, Counting Polyomino Tilings.

Formula

a(3) = A167243(3). a(4) = A167248(4). a(5) = A167251(5). a(6) = A167254(6). a(7) = A167255(7). a(8) = A167258(8). - R. J. Mathar, Oct 13 2024

Example

A 2 X 2 square can be covered by two dominoes by either positioning them vertically or horizontally.

Crossrefs

Intersects with A167251, A167254, A167255, A167258.

Diagonal of A348452.

Sequence in context: A356514 A006121 A110951 * A265942 A120597 A322295

Adjacent sequences: A172474 A172475 A172476 * A172478 A172479 A172480

Keyword

nonn,more

Author

Johan de Ruiter, Feb 04 2010

Extensions

a(9) from Bob Harris (me13013(AT)gmail.com), Mar 13 2010

a(10) from Jamie Tucker-Foltz (together with Jeanne Clelland, Edouard Heitzmann, and Gabe Schoenbach), Nov 16 2025

Status

approved