A383663 Number of closed knight's tours in the first 2n cells of a 7 X ceiling(2n/7) board.

2, 11, 58, 0, 21, 1020, 9309, 1481, 34162, 1295034, 1067638, 2213327, 50139185, 682189688, 144994543, 2607067351, 53099426601, 34524432316, 57716933870, 1388556345255, 16330667126220, 3697750041989, 70341043737487, 1662805965511580, 1250063279938854, 2122662114673944

Offset: 11

Author

Don Knuth, May 04 2025

Keywords

• nonn

Comments

If n is not a multiple of 7, the rightmost column has only 2n mod 7 rows (see example).

Examples

			For n=11, the first of a(11)=2 solutions is
  1  4 21  6
 20  7  2
  3 22  5
  8 19 10
 11 16 13
 14  9 18
 17 12 15
and the other is obtained by reflecting the bottom four rows:
  1  4 21  6
 20  7  2
  3 22  5
 10 19  8
 13 16 11
 18  9 14
 15 12 17 .
		

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..147
• Don Knuth, CWEB program with input parameter board,42,7,0,0,5,0,0.gb [the graph "board(50, 6, 0, 0, 5, 0, 0)" generated by the Stanford GraphBase].

Crossrefs

Cf. A193054, A383660, A383661, A383662, A383664.

Formula

a(7n) = A193054(n).