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A269757 Number of black cells after n moves of Langton's ant on an infinite hexagonal grid, starting with only white cells. 8
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 (list; graph; refs; listen; history; text; internal format)
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 * A245352 A099033 A187786

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

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Last modified November 15 22:20 EST 2018. Contains 317252 sequences. (Running on oeis4.)