The On-Line Encyclopedia of Integer Sequences (OEIS)

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A003763

Number of (undirected) Hamiltonian cycles on a 2n X 2n square grid of points.
(history; published version)

#90 by Michael De Vlieger at Sun Oct 29 10:50:55 EDT 2023

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reviewed

approved

#89 by Joerg Arndt at Sun Oct 29 08:24:13 EDT 2023

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proposed

reviewed

#88 by Michel Marcus at Sun Oct 29 06:13:08 EDT 2023

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editing

proposed

#87 by Michel Marcus at Sun Oct 29 06:12:54 EDT 2023

LINKS

Ville H. Pettersson, <a href="httphttps://www.combinatoricsdoi.org/ojs/index10.php/eljc/article/view37236/v21i4p74510">Enumerating Hamiltonian Cycles</a>, The Electronic Journal of Combinatorics, Volume 21, Issue 4, 2014.

#86 by Michel Marcus at Sun Oct 29 06:11:41 EDT 2023

LINKS

A. Pönitz, Pönitz, <a href="httphttps://wwwtubaf.qucosa.de/fileadmin/dataapi/qucosa%3A22459/documentsattachment/2080ATT-0/MathematikPXnitzAndrX756952.pdf">Über Über eine Methode zur Konstruktion...</a> PhD Thesis (2004) C.3.

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proposed

editing

#85 by Jon E. Schoenfield at Sun Oct 29 05:47:04 EDT 2023

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editing

proposed

#84 by Jon E. Schoenfield at Sun Oct 29 05:46:50 EDT 2023

NAME

Number of (undirected) Hamiltonian cycles on a 2n X 2n square grid of points.

LINKS

Artem M. Karavaev and N. J. A. Sloane, <a href="/A003763/b003763.txt">Table of n, a(n) for n = 1..13</a> [First (first 11 terms from Artem M. Karavaev, Sep 29 2010; a(12) and a(13) from Pettersson, 2014, added by N. J. A. Sloane, Jun 05 2015])

J. L. Jacobsen, <a href="http://dx.doi.org/10.1088/1751-8113/40/49/003">Exact enumeration of Hamiltonian circuits, walks and chains in two and three dimensions</a>, J. Phys. A: Math. Theor. 40 (2007) 14667-14678.

A. Pönitz, <a href="http://dx.doi.org/10.1016/S0378-4754(99)00052-X">Computing invariants in graphs of small bandwidth</a>, Mathematics in Computers and Simulation, 49(1999), 179-191.

N. J. A. Sloane, <a href="/A003763/a003763.jpg">Illustration of a(2) = 6</a>.

Peter Tittmann, <a href="http://www.htwm.de/~peter/research/enumeration.html">Enumeration in graphs: counting Hamiltonian cycles</a> . [Broken link?]

Peter Tittmann, <a href="http://web.archive.org/web/20101127064650/https://www.staff.hs-mittweida.de/~peter/research/enumeration.html">Enumeration in graphs: counting Hamiltonian cycles</a> . [Backup copy of top page only, on the Internet Archive]

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>.

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianCycle.html">Hamiltonian Cycle</a>.

<a href="/index/Gra#graphs">Index entries for sequences related to graphs, Hamiltonian</a>.

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approved

editing

#83 by Joerg Arndt at Wed Feb 17 10:52:19 EST 2021

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proposed

approved

#82 by Pontus von Brömssen at Wed Feb 17 10:43:58 EST 2021

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editing

proposed

#81 by Pontus von Brömssen at Wed Feb 17 10:43:27 EST 2021

LINKS

Artem M. Karavaev, <a href="https://web.archive.org/web/20161024010518/http://flowproblem.ru/cycles/hamilton-cycles">Hamilton Cycles</a>.

STATUS

approved

editing