A327131 Cells visited by knight moves on a spirally numbered infinite hexagonal board, moving to the lowest unvisited cell at each step.

1, 20, 6, 9, 4, 8, 5, 10, 13, 2, 14, 7, 11, 22, 3, 15, 12, 23, 26, 29, 16, 19, 34, 54, 17, 31, 50, 47, 24, 21, 18, 32, 35, 55, 30, 27, 45, 68, 25, 42, 39, 36, 33, 53, 78, 48, 51, 76, 106, 49, 73, 28, 46, 43, 40, 37, 58, 84, 87, 60, 63, 41, 69, 72, 101, 67, 44

Offset

1,2

Comments

The infinite hexagonal board is numbered spirally as:

.

17--18--19...

/

16 6---7---8

/ / \

15 5 1---2 9

\ \ / /

14 4---3 10

\ /

13--12--11

.

In Glinski's hexagonal chess, a knight (N) can move to these (o) cells:

.

. . . . .

. . o o . .

. o . . . o .

. o . . . . o .

. . . . N . . . .

. o . . . . o .

. o . . . o .

. . o o . .

. . . . .

.

This sequence is finite and ends at a(83966) = 72085 when the knight is "trapped".

Links

Sangeet Paul, Table of n, a(n) for n = 1..83966

Scott R. Shannon, Image showing the 83965 steps of the knight's path. The green central dot is the starting square and the red dot, located on the edge at the 7:30 clock position, the final square. Blue dots show the twelve occupied squares surrounding the final square. The lowest unvisited square, 71301, is the yellow dot on the edge at the 9:00 clock position.

Chess variants, Glinski's Hexagonal Chess

Wikipedia, Hexagonal chess - Gliński's hexagonal chess

Crossrefs

Cf. A316667, A327132.

Sequence in context: A161997 A274458 A351025 * A076594 A174991 A217418

Adjacent sequences: A327128 A327129 A327130 * A327132 A327133 A327134

Keyword

nonn,fini,full

Author

Sangeet Paul, Aug 22 2019

Status

approved