A391999 Number of undirected closed knight's tours on a 9 X (2n) board.

0, 0, 3374967940, 7112881119092574

Offset

1,3

References

Donald E. Knuth, Hamiltonian paths and cycles, Prefascicle 8a of The Art of Computer Programming (work in progress, 2025).

Links

Table of n, a(n) for n=1..4.

Donald E. Knuth, Adventures with Knight's Tours, Christmas lecture Dec. 2025.

Example

A closed knight's tour on a 9 X 6 board:
  a1_c2_e1_g2_i1_h3_i5_g6_h4_i6_g5_i4_h6_f5_d6_b5_a3_b1_d2_f1_h2_f3_g1_i2_g3_h1_i3_
  h5_f6_e4_f2_g4_e3_d1_b2_a4_b6_c4_a5_c6_e5_d3_c1_a2_c3_e2_d4_e6_f4_d5_b4_a6_c5_b3_a1

Crossrefs

Cf. A169764 (3Xn), A000004 (4Xn), A175855 (5Xn), A175881 (6Xn), A193054 (7Xn), A193055 (8Xn), A001230 (2nX2n), A392000 (kXn).

Sequence in context: A348811 A251523 A155961 * A282401 A063412 A384645

Adjacent sequences: A391996 A391997 A391998 * A392000 A392001 A392002

Keyword

nonn,more

Author

Peter Luschny, Dec 27 2025

Status

approved