A383662 Number of closed knight's tours in the first 2n cells of a 6 X ceiling(2n/6) board.

6, 0, 2, 302, 8, 151, 19072, 9862, 18202, 1603948, 1067638, 1310791, 107096187, 55488142, 66608924, 6149236417, 3374967940, 4259963914, 402706752421, 239187240144, 292999006211, 26470682075988, 15360134570696, 18595568012716, 1685811256230132, 964730606632516, 1173328484648288

Offset

11,1

Comments

If n is not a multiple of 3, the rightmost column has only 2n mod 6 rows (see example).

References

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

Links

Don Knuth, Table of n, a(n) for n = 11..150

Don Knuth, CWEB program with input parameter board,50,6,0,0,5,0,0.gb [the graph "board(50, 6, 0, 0, 5, 0, 0)" generated by the Stanford GraphBase].

Formula

a(3n) = A175881(n).

Example

For n=11, one of the a(11)=6 solutions is
  1  4 13 16
 12 15  2  5
  3 22 17 14
  8 11  6 19
 21 18  9
 10  7 20   .

Crossrefs

Cf. A175881, A383660, A383661, A383663, A383664.

Sequence in context: A075092 A152244 A283634 * A372064 A179641 A384466

Adjacent sequences: A383659 A383660 A383661 * A383663 A383664 A383665

Keyword

nonn

Author

Don Knuth, May 04 2025

Status

approved