A327132 Last cell visited by knight moves on a spirally numbered hexagonal board of edge-length n, moving to the lowest unvisited cell at each step.

1, 1, 1, 34, 45, 76, 98, 135, 181, 234, 290, 338, 413, 487, 566, 654, 742, 823, 930, 1051, 1169, 1291, 1414, 1548, 1685, 1813, 1968, 2138, 2304, 2455, 2632, 2815, 3016, 3187, 3388, 3597, 3803, 4026, 4246, 4473, 4714, 4948, 5194, 5447, 5702, 5969, 6244, 6514

Offset

1,4

Comments

A hexagonal board of edge-length 3, for example, 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 . .

. . . . .

.

a(n) stays constant at 72085 for n >= 177 since 72085 is also the last cell visited by knight moves on a spirally numbered infinite hexagonal board, moving to the lowest unvisited cell at each step.

Links

Sangeet Paul, Table of n, a(n) for n = 1..200

Chess variants, Glinski's Hexagonal Chess

Wikipedia, Hexagonal chess - Gliński's hexagonal chess

Crossrefs

Cf. A308312, A327131.

Sequence in context: A302457 A063470 A089715 * A260284 A274189 A275194

Adjacent sequences: A327129 A327130 A327131 * A327133 A327134 A327135

Keyword

nonn

Author

Sangeet Paul, Aug 22 2019

Status

approved