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

Author

Sangeet Paul, Aug 22 2019

Keywords

• nonn

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.