A383154 The number of 2n-by-2n fers-wazir tours.

2, 2, 22, 1620, 882130, 3465050546

Offset

1,1

Comments

The simplest fairy chess pieces, going back to 9th-century Persia, are the fers -- a (1,1) leaper -- and the wazir -- a (1,0) leaper. (A king combines the moves of a fers and a wazir.) A fers-wazir tour visits every cell of a board exactly once, making fers and wazir moves alternately, and returns to the starting cell.

Such tours exist only when the number of rows is even and the number of columns is even.

References

D. E. Knuth, Hamiltonian paths and cycles, Section 7.2.2.4 of The Art of Computer Programming (to appear).

Links

Table of n, a(n) for n=1..6.

George Jelliss, Introducing Knight's Tours, has a 9th century example of a fers-knight tour due to As-Suli.

Example

For n=2 the a(2) = 2 solutions are transposes of each other:
.
  0-f 4-3   0 e-d b
   X   X    |X   X|
  e 1-2 5   f 1 a c
  |     |     | |
  d a-9 6   4 2 9 7
   X   X    |X   X|
  b-c 7-8   3 5-6 8

Crossrefs

Diagonal of A383153.

Cf. A140519.

Sequence in context: A357244 A001012 A040082 * A014358 A093355 A122962

Adjacent sequences: A383151 A383152 A383153 * A383155 A383156 A383157

Keyword

nonn,more

Author

Don Knuth, Apr 18 2025

Status

approved