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Langton's ant on a snub square tiling: number of black cells after n moves of the ant when starting on a square.
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%I #23 Nov 27 2020 13:21:00

%S 0,1,2,3,4,5,4,5,6,7,8,9,8,9,10,11,10,9,10,11,12,13,14,13,14,15,16,15,

%T 16,17,18,17,16,17,18,17,16,15,16,17,18,17,16,17,18,19,20,21,20,21,22

%N Langton's ant on a snub square tiling: number of black cells after n moves of the ant when starting on a square.

%C First differs from A276073 at n = 16.

%C On a white square, turn 90 degrees right, flip the color of the tile, then move forward one unit.

%C On a white triangle, turn 60 degrees right, flip the color of the tile, then move forward one unit.

%C On a black square, turn 90 degrees left, flip the color of the tile, then move forward one unit.

%C On a black triangle, turn 60 degrees left, flip the color of the tile, then move forward one unit.

%H Lars Blomberg, <a href="/A309064/b309064.txt">Table of n, a(n) for n = 0..10000</a>

%H Lars Blomberg, <a href="/A309064/a309064.png">The state for n=104000, when 872 cells are set</a>

%H Lars Blomberg, <a href="/A309064/a309064_2.mp4">Animation illustrating n=1-3000</a>

%H Lars Blomberg, <a href="/A309064/a309064_1.mp4">Animation illustrating the transition from "chaos" to "avenue", n=96300-99608</a>

%H Felix Fröhlich, <a href="/A309064/a309064.pdf">Illustration of iterations 0-50 of the ant</a>, 2019.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Langton%27s_ant">Langton's ant</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Snub_square_tiling">Snub square tiling</a>

%F a(n+1025) = a(n) + 25 for n > 96420. _Lars Blomberg_, Aug 15 2019

%e See illustrations in Fröhlich, 2019.

%Y Cf. A255938, A269757, A276073, A308590, A308937, A308973, A326167, A326352.

%K nonn

%O 0,3

%A _Felix Fröhlich_, Jul 10 2019