login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A120443 Number of (undirected) Hamiltonian paths in the n X n grid graph. 18
1, 4, 20, 276, 4324, 229348, 13535280, 3023313284, 745416341496, 730044829512632, 786671485270308848, 3452664855804347354220, 16652005717670534681315580, 331809088406733654427925292528, 7263611367960266490262600117251524 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Jesper L. Jacobsen, Table of n, a(n) for n = 1..17
J. L. Jacobsen, Exact enumeration of Hamiltonian circuits, walks and chains in two and three dimensions, J. Phys. A: Math. Theor. 40 (2007) 14667-14678.
J.-M. Mayer, C. Guez and J. Dayantis, Exact computer enumeration of the number of Hamiltonian paths in small square plane lattices, Physical Review B, Vol. 42 Number 1, 1990.
Eric Weisstein's World of Mathematics, Grid Graph
Eric Weisstein's World of Mathematics, Hamiltonian Path
FORMULA
a(n) = A096969(n) / 2 for n > 1.
EXAMPLE
From Robert FERREOL, Apr 03 2019: (Start)
a(3) = 20:
there are 4 paths similar to
+ - + - +
|
+ - + - +
|
+ - + - +
8 paths similar to
+ - + - +
| |
+ + - +
| |
+ + - +
and 8 paths similar to
+ - + - +
| |
+ + +
| | |
+ + - +
(End)
CROSSREFS
Main diagonal of A332307.
Sequence in context: A222655 A000847 A188810 * A053400 A362259 A120599
KEYWORD
nonn,walk
AUTHOR
David Bevan, Jul 19 2006
EXTENSIONS
More terms from Jesper L. Jacobsen (jesper.jacobsen(AT)u-psud.fr), Dec 12 2007
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 07:21 EDT 2024. Contains 370955 sequences. (Running on oeis4.)