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 A140519 Number of "king tours" on an n X n board. 7
 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. 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. Ville Pettersson, Graph Algorithms for Constructing and Enumerating Cycles and Related Structures, Dissertation, Aalto, Finland, 2015. Eric Weisstein's World of Mathematics, Hamiltonian Cycle Eric Weisstein's World of Mathematics, King Graph CROSSREFS Cf. A001230, A140521. Sequence in context: A080273 A096404 A111824 * A285740 A174506 A109216 Adjacent sequences:  A140516 A140517 A140518 * A140520 A140521 A140522 KEYWORD nonn,walk AUTHOR Don Knuth, Jul 26 2008 STATUS approved

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