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A140519 Number of "king tours" on an n X n board. 6
1, 3, 16, 2830, 2462064, 22853860116, 1622043117414624, 961742089476282321684, 4601667243759511495116347104, 179517749570891592016479828267003018, 56735527086758553613684823040730404215973136, 145328824470156271670635015466987199469360063082789418 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Or, number of Hamiltonian cycles in the graph P_n X P_n.

If the direction of the tour is to be taken into account, the numbers for n > 1 must be multiplied by 2 (see A140521).

Computed using ZDDs (ZDD = "reduced, order, zero-suppressed binary decision diagram").

REFERENCES

D. E. Knuth, The Art of Computer Programming, Section 7.1.4, in preparation.

Ville Pettersson, Graph Algorithms for Constructing and Enumerating Cycles and Related Structures, Dissertation, Aalto, Finland, 2015; https://aaltodoc.aalto.fi/bitstream/handle/123456789/17688/isbn9789526063652.pdf?sequence=1

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..16 [From Pettersson 2014]

Ville H. Pettersson, Enumerating Hamiltonian Cycles, The Electronic Journal of Combinatorics, Volume 21, Issue 4, 2014.

Index entries for sequences related to graphs, Hamiltonian

CROSSREFS

Cf. A001230, A140521.

Sequence in context: A080273 A096404 A111824 * A174506 A109216 A090478

Adjacent sequences:  A140516 A140517 A140518 * A140520 A140521 A140522

KEYWORD

nonn,walk

AUTHOR

Don Knuth, Jul 26 2008

STATUS

approved

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Last modified December 10 00:24 EST 2016. Contains 278993 sequences.