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A325954 Langton's ant on a three-dimensional grid: number of blue cells on the grid after n moves of the ant.

%I A325954 #28 Jul 16 2025 17:54:56
%S A325954 0,0,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,1,2,2,3,4,4,3,3,3,3,3,3,3,4,4,4,5,
%T A325954 5,5,5,4,4,4,5,5,5,5,4,5,6,6,7,8,8,7,7,7,7,7,7,7,8,8,8,9,9,9,9,8,9,10,
%U A325954 9,9,10,10,10,10,9,8,8,8,7,8,8,8,8,7,8,9
%N A325954 Langton's ant on a three-dimensional grid: number of blue cells on the grid after n moves of the ant.
%C A325954 The ant starts on a completely white grid.
%C A325954 Order of operations: turn 90 degrees, change cell color, move forward one unit.
%C A325954 The rules governing the movement of the ant and the change of cell colors are shown in the following table:
%C A325954 Cell color at      | Direction of   | Color the cell is
%C A325954 start of iteration | 90-degree turn | changed to
%C A325954 --------------------------------------------------------
%C A325954 white              | right          | black
%C A325954 black              | left           | blue
%C A325954 blue               | up             | yellow
%C A325954 yellow             | down           | white
%H A325954 Jinyuan Wang, <a href="/A325954/b325954.txt">Table of n, a(n) for n = 0..10000</a>
%H A325954 Felix Fröhlich, <a href="/A325953/a325953_2.pdf">Illustration of iterations 0-50 of the ant</a>
%H A325954 Wikipedia, <a href="https://en.wikipedia.org/wiki/Langton%27s_ant">Langton's ant</a>
%F A325954 a(n) = a(n-28) + 2 for n >= 93504. - _Jinyuan Wang_, Jul 13 2025
%e A325954 See illustration in links.
%Y A325954 Cf. A255938, A308563, A325953, A325955.
%K A325954 nonn
%O A325954 0,19
%A A325954 _Felix Fröhlich_, May 28 2019
%E A325954 a(51)-a(80) from _Charlie Neder_, Jun 06 2019