%I #13 Feb 03 2023 02:41:31
%S 0,1,2,3,4,3,4,5,6,7,6,7,8,9,10,11,10,9,8,7,8,9,8,7,8,9,10,11,12,11,
%T 10,11,12,13,12,13,14,15,16,17,18,17,18,19,20,21,20,19,20,19,18,17,18,
%U 19,18,17,16,15,14,15,16,15,14,15,16,17,18,17,16,15,14
%N Langton's ant on a tiling with vertex types (4.6.12; 3.4.6.4), a(n) is number of black cells after n moves of the ant when starting on a dodecagon and looking towards an edge where the dodecagon meets a hexagon.
%C Rules for Langton's ant on edge-to-edge tilings by regular polygons: Initially, all tiles are white. On a white tile turn right, on a black tile turn left. Always flip the color of the tile, then move forward one unit. The turn angle for (triangle, square, hexagon, octagon, dodecagon) is (60, 90, 60, 45, 30).
%C After 276 steps all tiles are again white and the ant is on the starting tile heading in the starting direction, so the sequence repeats with a cycle length of 276.
%C Many other starting positions are possible which give different terms. While they all eventually repeat the cycle, lengths vary (68, 96, 276, 1320, 2092).
%H Lars Blomberg, <a href="/A322290/b322290.txt">Table of n, a(n) for n = 0..276</a>
%F a(n+276) = a(n).
%K nonn
%O 0,3
%A _Lars Blomberg_, Aug 28 2019