A383661 Number of closed knight's tours in the first 2n cells of a 5 X ceiling(2n/5) board.

1, 0, 1, 30, 0, 148, 8, 78, 9309, 612, 62749, 44202, 42049, 2916485, 147192, 18284136, 13311268, 13008389, 973107552, 51147756, 6190192748, 4557702762, 4311375354, 316985255470, 16552301184, 2015267424300, 1495135512514, 1417634375316, 104324890543686, 5459334927260, 663068761241948

Offset: 9

Author

Don Knuth, May 04 2025

Keywords

• nonn

Comments

If n is not a multiple of 5, the rightmost column has only 2n mod 5 rows (see example).

Examples

			For n=9 the a(9)=1 example is
  1 14  5 10
  4  9  2 15
 13 18 11  6
  8  3 16
 17 12  7    .
		

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 = 9..150
• Don Knuth, CWEB program with input parameter board,60,5,0,0,5,0,0.gb [the graph "board(50, 6, 0, 0, 5, 0, 0)" generated by the Stanford GraphBase].

Crossrefs

Cf. A175855, A383660, A383662, A383663, A383664.

Formula

a(5n) = A175855(n).