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A140521 Number of directed "king tours" on an n X n board. 4
1, 6, 32, 5660, 4924128, 45707720232, 3244086234829248, 1923484178952564643368 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

If the direction of the tour is not taken into account, the numbers for n > 1 must be halved (see A140519).

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

Table of n, a(n) for n=1..8.

Eric Weisstein's World of Mathematics, Hamiltonian Cycle

Eric Weisstein's World of Mathematics, King Graph

Index entries for sequences related to graphs, Hamiltonian

CROSSREFS

Cf. A001230, A140519.

Sequence in context: A222605 A222749 A132548 * A171141 A069065 A073343

Adjacent sequences:  A140518 A140519 A140520 * A140522 A140523 A140524

KEYWORD

nonn,walk

AUTHOR

Don Knuth, Jul 26 2008

STATUS

approved

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Last modified December 9 06:30 EST 2016. Contains 278963 sequences.