A383664 Number of closed knight's tours in the first 2n cells of an 8 X ceiling(2n/8) board.

4, 12, 212, 0, 50, 4525, 101730, 44202, 66034, 2408624, 69362264, 55488142, 101343548, 2398536889, 43391615822, 34524432316, 52661182514, 1231713564493, 20780788492646, 13267364410532, 21515340977481, 552407941427835, 10211663162678661, 7112881119092574, 11873618786859165

Offset: 13

Author

Don Knuth, May 04 2025

Keywords

• nonn

Comments

If n is not a multiple of 4, the rightmost column has only 2n mod 8 rows (see example).

Examples

			For n=13 the a(13)=4 solutions are
  1  4 25 12
 24 11  2  5
  3 26 13
 10 23  6
  7 14  9
 22 17 20
 19  8 15
 16 21 18   ;
  1  4 25 12
 24 11  2  5
  3 26 13
 10 23  6
  7 14  9
 20 15 22
 15  8 19
 18 21 16   ;
  1 14 25 22
 24 21  2 15
 13 26 23
 20  3 16
 17 12 19
  4  9  6
  7 18 11
 10  5  8   ;
  1 14 25 22
 24 21  2 15
 13 26 23
 20  3 16
 17 12 19
  6  9  4
 11 18  7
  8  5 10   .
		

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 = 13..96
• Don Knuth, CWEB program with input parameter board,32,8,0,0,5,0,0.gb [the graph "board(50, 6, 0, 0, 5, 0, 0)" generated by the Stanford GraphBase].

Crossrefs

Cf. A193055, A383660, A383661, A383662, A383663.

Formula

a(4n) = A193055(n).