

A327131


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


4



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
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OFFSET

1,2


COMMENTS

The infinite hexagonal board is numbered spirally as:
.
171819...
/
16 678
/ / \
15 5 12 9
\ \ / /
14 43 10
\ /
131211
.
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

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.


CROSSREFS



KEYWORD

nonn,fini,full


AUTHOR



STATUS

approved



