A269757 Number of black cells after n moves of Langton's ant on an infinite hexagonal grid, starting with only white cells.

0, 1, 2, 3, 4, 5, 6, 5, 6, 7, 8, 9, 8, 7, 8, 9, 10, 11, 10, 9, 10, 11, 12, 13, 12, 13, 14, 15, 16, 17, 18, 17, 16, 17, 18, 19, 20, 19, 18, 19, 20, 21, 22, 21, 20, 19, 18, 19, 20, 21, 22, 21, 20, 21, 22, 23, 24, 23, 22, 21, 20, 21, 22, 23, 24, 23, 22, 23, 24, 25, 26

Offset

0,3

Comments

On a white cell, turn 60 degrees right, flip the color of the cell, then move forward one unit. On a black cell, turn 60 degrees left, flip the color of the cell, then move forward one unit.

One may see the ant as (1) living on a hexagonal tiling (as in the illustration), in which case one third of all tiles are never visited, or (2) as living on a triangular tiling, in which case these never-visited hexagonal tiles are divided between six neighboring tiles to form triangular tiles, or (3) as living on a hexagonal grid understood as a graph dual to that triangular tiling, in which case the ant travels from one vertex to another using edges. - Andrey Zabolotskiy, Oct 09 2016

Links

Oleg Nikulin, Table of n, a(n) for n = 0..10000

Felix Fröhlich, Illustration of a(0)-a(19)

Wikipedia, Langton's ant

Crossrefs

Cf. A255938, A275302-A275305.

Sequence in context: A071532 A102730 A165597 * A308973 A309279 A245352

Adjacent sequences: A269754 A269755 A269756 * A269758 A269759 A269760

Keyword

nonn

Author

Felix Fröhlich, Mar 04 2016

Extensions

More terms from Oleg Nikulin, Jul 22 2016

Status

approved