

A348456


Number of ways to dissect a 2*n X 2*n chessboard into two polyominoes each of area 2*n^2.


12



1, 2, 70, 80518, 7157114189, 49852157614583644, 28289358593043414725944353, 1335056579423080371186456888543732162, 5288157175943649955880910966508435029578848399795, 1768514227824943648668138153226998430209626836775021539911012000, 50126261987194138333095266040242179892262270498222242227767710277119489194126252, 120727080026653995683405108506109122788592972611035310673809853406496349171003311517916839962975062
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OFFSET

0,2


COMMENTS

See A348453 for much more information.
The board has 4*n^2 squares. The colors of the squares do not matter. The two parts are rookconnected polygons of area 2*n^2. They do not need to be the same polygon, only that they have the same area.
This is the "labeled" version of the problem. Symmetries of the square are not taken into account. Rotations and reflections count as different.
a(4) was found on May 04 2022 by George Spahn and Manuel Kauers using an 1838 X 1838 transfer matrix found by George Spahn (see the Zeilberger link). Manuel Kauers computed the [1,2] entry of the 9th power of that matrix. The desired number a(4) is half of the coefficient of z^32 in that entry.  Doron Zeilberger, May 04 2022
Also known as the "Gerrymander Sequence" per Kauers, et al.  Michael De Vlieger, Dec 06 2022


LINKS



CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS

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).


STATUS

approved



