A395362 - OEIS

A395362

Walk along the hexagonal spiral, with its cells numbered starting at 0. Begin with no knights. If the square you are at is not attacked by an existing knight, place a knight there, otherwise leave it empty. The sequence lists the squares occupied by the knights.

0, 1, 2, 3, 4, 5, 6, 40, 44, 48, 52, 56, 60, 61, 64, 65, 66, 69, 70, 71, 74, 75, 76, 79, 80, 81, 84, 85, 86, 89, 90, 91, 95, 96, 97, 101, 102, 103, 107, 108, 109, 113, 114, 115, 119, 120, 121, 125, 126, 220, 221, 225, 229, 230, 234, 238, 239, 243, 247, 248, 252, 256, 257, 261, 265, 266, 270, 271, 274, 275, 276, 279, 280, 281, 284

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

This sequence is based on a tiling of the plane by hexagons (often called the hexagonal lattice), with the cells numbered in a counter-clockwise hexagonal spiral starting with index 0. A028896 has a picture of the beginning of the spiral, except that there the cells are numbered clockwise.

The knights are Glinski knights for playing hexagonal chess, which can move two steps in any of the six directions followed by a further step at sixty degrees, and so can move to any of 12 cells (see illustration).

This is the analog for the hexagonal spiral of the square spiral sequence A308885. In the latter spiral the knights are classical chess knights.

LINKS

Jonas Karlsson, Table of n, a(n) for n = 0..19999

Jonas Karlsson, 133 knights drawn together with the spiral. The knights are black circles.

N. J. A. Sloane, The hexagonal cells 0 to 63 at the start of the spiral. The numbers are at the centers of the hexagons (which are not shown).

N. J. A. Sloane, The 12 possible moves (O) for a Glinski knight (N) on the hexagonal grid.

N. J. A. Sloane, The center of the spiral, showing the first 64 cells.

N. J. A. Sloane, The first 128 cells of the spiral (Left half). The cells with knights are colored red.

N. J. A. Sloane, The first 128 cells of the spiral (Right half). The cells with knights are colored red.

CROSSREFS

Cf. A028896, A308885, A327131, A333683.

See A395365-A395367 for what happens when there are knights of two colors.