A172477
The number of ways to dissect an n X n square into polyominoes of size n.
Original entry on oeis.org
1, 2, 10, 117, 4006, 451206, 158753814, 187497290034, 706152947468301
Offset: 1
A 2 X 2 square can be covered by two dominoes by either positioning them vertically or horizontally.
- Jiahua Chen, Aneesha Manne, Rebecca Mendum, Poonam Sahoo, 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 [From Bob Harris (me13013(AT)gmail.com), Mar 13 2010]
a(9) from Bob Harris (me13013(AT)gmail.com), Mar 13 2010
A167242
Number of ways to partition a 2*n X 3 grid into 2 connected equal-area regions.
Original entry on oeis.org
1, 3, 19, 85, 355, 1435, 5717, 22645, 89521, 353735, 1397863, 5525341, 21846421, 86403027, 341822335, 1352660761, 5354124895, 21197945407, 83945924393, 332507403625, 1317329758675, 5220055148883, 20688989887169, 82013159349085, 325165555406795, 1289434099001055, 5114044079094817, 20286061330030705, 80481556028898031
Offset: 0
Some solutions for n=4
...1.1.1...1.1.1...1.1.2...1.1.2...1.1.2...1.1.1...1.1.1...1.1.1...1.1.1
...1.1.1...1.1.2...1.2.2...1.1.2...1.2.2...2.2.1...1.1.1...2.1.1...1.1.1
...2.2.1...1.2.2...1.1.2...1.2.2...1.2.2...2.2.1...2.1.1...2.2.1...2.1.1
...2.1.1...1.2.2...1.2.2...1.2.2...1.1.2...2.2.1...2.2.1...2.1.1...2.2.1
...2.2.1...1.2.2...1.1.2...1.2.2...1.1.2...2.1.1...2.2.1...2.2.1...2.2.1
...2.2.1...1.1.2...1.1.2...1.2.2...1.1.2...2.1.1...2.1.1...2.1.1...2.2.1
...2.2.1...1.2.2...1.2.2...1.1.2...1.1.2...2.1.1...2.2.2...2.1.2...2.2.1
...2.2.2...1.2.2...1.2.2...1.1.2...2.2.2...2.2.2...2.2.2...2.2.2...2.2.2
- D. E. Knuth (Proposer) and Editors (Solver), Balanced tilings of a rectangle with three rows, Problem 11929, Amer. Math. Monthly, 125 (2018), 566-568.
- Manuel Kauers, Christoph Koutschan, and George Spahn, A348456(4) = 7157114189, arXiv:2209.01787 [math.CO], 2022.
- Manuel Kauers, Christoph Koutschan, and George Spahn, How Does the Gerrymander Sequence Continue?, J. Int. Seq., Vol. 25 (2022), Article 22.9.7.
Showing 1-2 of 2 results.