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

Author

Don Knuth, May 04 2025

Keywords

• nonn

Comments

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

Examples

			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    .
		

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.

Crossrefs

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

Formula

a(3n) = A070030(n).