cp's OEIS Frontend

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.

A001230 Number of undirected closed knight's tours on a 2n X 2n chessboard.

This page as a plain text file.
%I A001230 #57 Feb 16 2025 08:32:23
%S A001230 0,0,9862,13267364410532
%N A001230 Number of undirected closed knight's tours on a 2n X 2n chessboard.
%C A001230 No closed tour exists on an m X m board if m is odd.
%D A001230 Brendan McKay, personal communication, Feb 03, 1997.
%D A001230 W. W. Rouse Ball, Mathematical Recreations and Essays (various editions), Chap. 6.
%D A001230 I. Wegener, Branching Programs and Binary Decision Diagrams, SIAM, Philadelphia, 2000; see p. 369.
%H A001230 G. L. Chia, Siew-Hui Ong, <a href="http://dx.doi.org/10.1016/j.dam.2004.11.008">Generalized knight's tour on rectangular chessboards</a>, Disc. Appl. Math. 150(1-3) (2005) 80-98.
%H A001230 N. D. Elkies and R. P. Stanley, <a href="http://dx.doi.org/10.1007/BF02985635">The mathematical knight</a>, Math. Intelligencer, 25 (No. 1) (2003), 22-34.
%H A001230 Brady Haran, <a href="http://www.youtube.com/watch?v=ab_dY3dZFHM">Knight's Tour</a>, Numberphile video (2014).
%H A001230 George Jelliss, <a href="http://www.mayhematics.com/t/t.htm">Knight's Tour Notes</a>
%H A001230 Stoyan Kapralov, Valentin Bakoev, and Kaloyan Kapralov, <a href="https://arxiv.org/abs/1711.06792">Enumeration of Some Closed Knight Paths</a>, arXiv preprint arXiv:1711.06792 [math.CO], 2017.
%H A001230 M. Loebbing and I. Wegener, <a href="https://doi.org/10.37236/1229">The Number of Knight's Tours Equals 33,439,123,484,294 -- Counting with Binary Decision Diagrams</a>. Electronic Journal of Combinatorics 3 (1996), R5. [The number given in the paper is incorrect, see <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v3i1r5/comment">comments</a>.]
%H A001230 B. D. McKay, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/downloadSuppFile/v3i1r5/mckay">"Knight's Tours of an 8x8 Chessboard"</a>. Technical Report TR-CS-97-03, Department of Computer Science, Australian National University (1997). [<a href="/A001230/a001230.pdf">Cached copy</a>, with permission]
%H A001230 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HamiltonianCycle.html">Hamiltonian Cycle</a>
%H A001230 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KnightGraph.html">Knight Graph</a>
%H A001230 Wikipedia, <a href="http://en.wikipedia.org/wiki/Knights_tour">Knight's tour</a>
%t A001230 Table[Length[FindHamiltonianCycle[KnightTourGraph[2 n, 2 n], All]], {n, 3}]
%Y A001230 Cf. A165134.
%K A001230 nonn,hard,more,nice
%O A001230 1,3
%A A001230 _N. J. A. Sloane_, Martin Loebbing (loebbing(AT)ls2.informatik.uni-dortmund.de), _Brendan McKay_
%E A001230 Loebbing and Wegener incorrectly gave 33439123484294 for the 8 X 8 board. The value given here is due to _Brendan McKay_ and agrees with that given by Wegener in his book.
%E A001230 Description and links corrected by _Max Alekseyev_, Dec 09 2008