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

Author

Don Knuth, May 04 2025

Keywords

• nonn

Comments

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

Examples

			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   .
		

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].

Crossrefs

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

Formula

a(3n) = A175881(n).