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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.

%I A269757 #18 Nov 07 2016 02:09:52
%S A269757 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,
%T A269757 16,17,18,17,16,17,18,19,20,19,18,19,20,21,22,21,20,19,18,19,20,21,22,
%U A269757 21,20,21,22,23,24,23,22,21,20,21,22,23,24,23,22,23,24,25,26
%N A269757 Number of black cells after n moves of Langton's ant on an infinite hexagonal grid, starting with only white cells.
%C A269757 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.
%C A269757 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
%H A269757 Oleg Nikulin, <a href="/A269757/b269757.txt">Table of n, a(n) for n = 0..10000</a>
%H A269757 Felix Fröhlich, <a href="/A269757/a269757.pdf">Illustration of a(0)-a(19)</a>
%H A269757 Wikipedia, <a href="https://en.wikipedia.org/wiki/Langton%27s_ant">Langton's ant</a>
%Y A269757 Cf. A255938, A275302-A275305.
%K A269757 nonn
%O A269757 0,3
%A A269757 _Felix Fröhlich_, Mar 04 2016
%E A269757 More terms from _Oleg Nikulin_, Jul 22 2016