This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A348456 #51 Aug 29 2025 11:07:44 %S A348456 1,2,70,80518,7157114189,49852157614583644,28289358593043414725944353, %T A348456 1335056579423080371186456888543732162, %U A348456 5288157175943649955880910966508435029578848399795,1768514227824943648668138153226998430209626836775021539911012000,50126261987194138333095266040242179892262270498222242227767710277119489194126252,120727080026653995683405108506109122788592972611035310673809853406496349171003311517916839962975062 %N A348456 Number of ways to dissect a 2*n X 2*n chessboard into two polyominoes each of area 2*n^2. %C A348456 See A348453 for much more information. %C A348456 The board has 4*n^2 squares. The colors of the squares do not matter. The two parts are rook-connected polygons of area 2*n^2. They do not need to be the same polygon, only that they have the same area. %C A348456 This is the "labeled" version of the problem. Symmetries of the square are not taken into account. Rotations and reflections count as different. %C A348456 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 %C A348456 Also known as the "Gerrymander Sequence" per Kauers, et al. - _Michael De Vlieger_, Dec 06 2022 %H A348456 Anthony J. Guttmann and Iwan Jensen, <a href="https://arxiv.org/abs/2211.14482">The gerrymander sequence, or A348456</a>, arXiv:2211.14482 [math.CO], 2022. %H A348456 Manuel Kauers, <a href="http://www.algebra.uni-linz.ac.at/people/mkauers/publications/kauers25j.pdf">D-Finiteness: A Success Story</a>, Experimental Math., Johannes Kepler Univ. (Austria, 2025). See p. 6. %H A348456 Manuel Kauers, Christoph Koutschan, and George Spahn, <a href="https://arxiv.org/abs/2209.01787">A348456(4) = 7157114189</a>, arXiv:2209.01787 [math.CO], 2022. %H A348456 Manuel Kauers, Christoph Koutschan, and George Spahn, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL25/Kauers/kauers6.html">How Does the Gerrymander Sequence Continue?</a>, J. Int. Seq., Vol. 25 (2022), Article 22.9.7. %H A348456 N. J. A. Sloane, <a href="https://vimeo.com/704569041/4ffa06b95e">The On-Line Encyclopedia of Integer Sequences: An illustrated guide with many unsolved problems</a>, Guest Lecture given in Doron Zeilberger's Experimental Mathematics Math640 Class, Rutgers University, Spring Semester, Apr 28 2022: <a href="https://sites.math.rutgers.edu/~zeilberg/EM22/C27.pdf">Slides</a>; <a href="http://NeilSloane.com/doc/Math640.04.2022.pdf">Slides (an alternative source)</a>. %H A348456 Doron Zeilberger, <a href="https://sites.math.rutgers.edu/~zeilberg/ChessChallenge.txt">Challenge to Manuel Kauers and his computer</a>. %Y A348456 A column of A348452 and A348453, and a diagonal of A348454 and A348455. %Y A348456 See also A358289. %Y A348456 Cf. A167242. %K A348456 nonn,changed %O A348456 0,2 %A A348456 _N. J. A. Sloane_, Oct 27 2021 %E A348456 Added a(5)-a(7) (from the Kauers et al. reference), _Joerg Arndt_, Sep 07 2022 %E A348456 a(8)-a(11) from Guttmann and Jensen (2022). %E A348456 a(0)=1 prepended by _Alois P. Heinz_, Dec 06 2022