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A120443 Number of (undirected) Hamiltonian paths in the n X n grid graph. 16
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

Index entries for sequences related to graphs, Hamiltonian

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.

Cf. A003685, A003695, A003778, A145402.

Cf. A003763, A000532, A001184, A145157, A271507, A007764, A121785, A121789.

Sequence in context: A222655 A000847 A188810 * A053400 A120599 A012797

Adjacent sequences: A120440 A120441 A120442 * A120444 A120445 A120446

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

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Last modified December 5 15:27 EST 2022. Contains 358588 sequences. (Running on oeis4.)