A383660 Number of closed knight's tours in the first 2n cells of a 3 X ceiling(2n/3) board.

4, 0, 4, 24, 16, 56, 306, 176, 456, 2632, 1536, 4828, 26788, 15424, 44952, 254288, 147728, 448032, 2502568, 1448416, 4310048, 24228704, 14060048, 42195584, 236335248, 136947616, 409403328, 2297294496, 1332257856, 3989883552, 22366625344, 12965578752, 38798663104, 217604833360, 126169362176

Offset

11,1

Comments

If n is not a multiple of 3, the rightmost column has only 2n mod 3 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,100,3,0,0,5,0,0.gb [the graph "board(50, 6, 0, 0, 5, 0, 0)" generated by the Stanford GraphBase.

Formula

a(3n) = A070030(n).

Example

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

Crossrefs

Cf. A070030, A383661, A383662, A383663, A383664.

Sequence in context: A058493 A112149 A087736 * A005075 A103638 A129821

Adjacent sequences: A383657 A383658 A383659 * A383661 A383662 A383663

Keyword

nonn

Author

Don Knuth, May 04 2025

Status

approved