cp's OEIS Frontend

A309293 Langton's ant on a snub trihexagonal tiling: number of black cells after n moves of the ant when starting on a hexagon.

%I A309293 #28 Jan 01 2024 22:47:26
%S A309293 0,1,2,3,4,5,4,5,6,7,8,9,10,11,12,11,10,11,12,13,14,15,14,15,16,17,18,
%T A309293 19,20,21,20,19,18,17,16,15,14,13,14,13,12,11,10,9,10,11,12,13,14,15,
%U A309293 16,17,16,15,16,17,18,17,16,17,18,19,18,17,16,15,14,15
%N A309293 Langton's ant on a snub trihexagonal tiling: number of black cells after n moves of the ant when starting on a hexagon.
%C A309293 On a white tile, turn 60 degrees right, flip the color of the tile, then move forward one unit.
%C A309293 On a black tile, turn 60 degrees left, flip the color of the tile, then move forward one unit.
%C A309293 The sequence has a cycle of length of 28292, that is, a(28292)=0 with the ant in the starting hexagon pointing in the start direction, so another cycle will follow. The maximum term in the cycle is a(8148)=174. - _Lars Blomberg_, Aug 01 2019
%H A309293 Lars Blomberg, <a href="/A309293/b309293.txt">Table of n, a(n) for n = 0..28292</a>
%H A309293 Lars Blomberg, <a href="/A309293/a309293.jpg">The state for n=8148, when 174 cells are set</a>
%H A309293 Lars Blomberg, <a href="/A309293/a309293.mp4">Video illustrating a full cycle</a>
%H A309293 Felix Fröhlich, <a href="/A309293/a309293.pdf">Illustration of iterations 0-50 of the ant</a>, 2019.
%H A309293 Wikipedia, <a href="https://en.wikipedia.org/wiki/Langton%27s_ant">Langton's ant</a>
%H A309293 Wikipedia, <a href="https://en.wikipedia.org/wiki/Snub_trihexagonal_tiling">Snub trihexagonal tiling</a>
%e A309293 See illustrations in Fröhlich, 2019.
%Y A309293 Cf. A255938, A269757, A308590, A308937, A308973, A326167, A326352, A309064, A309166, A309241, A309279.
%K A309293 nonn
%O A309293 0,3
%A A309293 _Felix Fröhlich_, Jul 21 2019
%E A309293 More terms from _Lars Blomberg_, Aug 01 2019