A348456
Number of ways to dissect a 2*n X 2*n chessboard into two polyominoes each of area 2*n^2.
Original entry on oeis.org
1, 2, 70, 80518, 7157114189, 49852157614583644, 28289358593043414725944353, 1335056579423080371186456888543732162, 5288157175943649955880910966508435029578848399795, 1768514227824943648668138153226998430209626836775021539911012000, 50126261987194138333095266040242179892262270498222242227767710277119489194126252, 120727080026653995683405108506109122788592972611035310673809853406496349171003311517916839962975062
Offset: 0
- Anthony J. Guttmann and Iwan Jensen, The gerrymander sequence, or A348456, arXiv:2211.14482 [math.CO], 2022.
- Manuel Kauers, D-Finiteness: A Success Story, Experimental Math., Johannes Kepler Univ. (Austria, 2025). See p. 6.
- 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.
- N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences: An illustrated guide with many unsolved problems, Guest Lecture given in Doron Zeilberger's Experimental Mathematics Math640 Class, Rutgers University, Spring Semester, Apr 28 2022: Slides; Slides (an alternative source).
- Doron Zeilberger, Challenge to Manuel Kauers and his computer.
Added a(5)-a(7) (from the Kauers et al. reference),
Joerg Arndt, Sep 07 2022
a(8)-a(11) from Guttmann and Jensen (2022).
A167243
Number of ways to partition an n X 3 grid into 3 connected equal-area regions.
Original entry on oeis.org
1, 3, 10, 23, 56, 132, 259, 546, 1095, 2043, 3908, 7379, 13208, 24194, 43819, 76790, 136489, 241311, 416152, 726073, 1261696, 2153026, 3706393, 6364842, 10775173, 18374181
Offset: 1
All solutions for n=4
...1.1.2...1.1.2...1.1.2...1.1.2...1.1.2...1.1.2...1.1.1...1.1.1...1.1.1
...1.2.2...1.2.2...1.1.2...1.1.2...1.3.2...3.1.2...1.2.2...1.2.2...1.2.2
...1.2.3...1.3.2...3.2.2...3.3.2...1.3.2...3.1.2...2.2.3...3.2.2...3.3.2
...3.3.3...3.3.3...3.3.3...3.3.2...3.3.2...3.3.2...3.3.3...3.3.3...3.3.2
------
...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.2.2...1.2.2
...1.2.3...2.2.1...2.2.1...2.2.1...2.1.3...2.1.3...2.3.1...1.2.2...1.2.2
...2.2.3...2.2.3...2.3.3...3.2.2...2.2.3...2.3.3...2.3.3...1.1.3...1.3.3
...2.3.3...3.3.3...2.3.3...3.3.3...2.3.3...2.2.3...2.2.3...3.3.3...1.3.3
------
...1.2.2...1.2.2...1.2.2...1.2.2...1.2.3
...1.2.3...1.1.2...1.1.2...1.3.2...1.2.3
...1.2.3...1.3.2...3.1.2...1.3.2...1.2.3
...1.3.3...3.3.3...3.3.3...1.3.3...1.2.3
A167247
Number of ways to partition an n X 4 grid into 2 connected equal-area regions.
Original entry on oeis.org
1, 4, 19, 70, 245, 856, 2967, 10164, 34463, 115904, 387379, 1288574, 4270853, 14116936, 46567963, 153385198
Offset: 1
All solutions for n=3
...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1
...1.1.2.2...1.2.1.2...1.2.2.1...1.2.2.2...2.1.1.2...2.1.2.1...2.2.1.1
...2.2.2.2...2.2.2.2...2.2.2.2...1.2.2.2...2.2.2.2...2.2.2.2...2.2.2.2
------
...1.1.1.1...1.1.1.2...1.1.1.2...1.1.1.2...1.1.1.2...1.1.2.2...1.1.2.2
...2.2.2.1...1.1.1.2...1.1.2.2...1.2.1.2...1.2.2.2...1.1.1.2...1.1.2.2
...2.2.2.1...2.2.2.2...1.2.2.2...1.2.2.2...1.1.2.2...1.2.2.2...1.1.2.2
------
...1.1.2.2...1.2.2.2...1.2.2.2...1.2.2.2...1.2.2.2
...1.2.2.2...1.1.1.2...1.1.2.2...1.2.1.2...1.2.2.2
...1.1.1.2...1.1.2.2...1.1.1.2...1.1.1.2...1.1.1.1
- 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.
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