A395446 Number of Hamiltonian paths on an n X n grid, starting from a fixed corner cell and ending anywhere, where the allowed moves are (+-3,0), (0,+-3), or (+-2,+-2).

1, 0, 0, 0, 552, 302282, 468698008

Offset

1,5

Comments

The 8 allowed moves are: 3 steps horizontally or vertically, or 2 steps diagonally (in all directions). Each cell must be visited exactly once. The path starts at a fixed corner cell and may end anywhere. This sequence arises from a traditional puzzle game played on paper in the Lombardy region (Italy), traditionally played on a 10 X 10 board.

A newt is a fairy chess piece which can move 3 steps orthogonally or 2 steps diagonally, so a(n) is the number of (not necessarily closed) newt's tours starting in a specified corner square of an n X n chessboard. - Pontus von Brömssen, May 01 2026

Links

Table of n, a(n) for n=1..7.

Robert P. P. McKone, The a(5) = 552 Hamiltonian paths.

Wikipedia, List of fairy chess pieces.

Crossrefs

Cf. A165134 (knight's tours, allowing arbitrary starting and ending positions).

Sequence in context: A290048 A023914 A035849 * A028686 A247531 A171428

Adjacent sequences: A395443 A395444 A395445 * A395447 A395448 A395449

Keyword

nonn,hard,more,walk

Author

Davide Limonta, Apr 23 2026

Status

approved