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A322567
Langton's ant on a tiling with vertex types (3.12.12; 3.4.3.12): number of black cells after n moves of the ant when starting on a dodecagon and looking towards an edge where it meets another dodecagon.
1
0, 1, 2, 3, 4, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 8, 9, 10, 11, 12, 11, 12, 13, 14, 15, 16, 17, 18, 19, 18, 17, 16, 15, 14, 15, 14, 15, 16, 17, 18, 19, 20, 19, 20, 21, 22, 23, 24, 25, 24, 25, 26, 27, 28, 27, 26, 27, 28, 29, 30, 31, 30, 29, 30, 31, 32
OFFSET
0,3
COMMENTS
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).
At n=66285 the ant starts a highway along the SE diagonal.
Many other starting positions are possible which give different terms. While they all eventually enter the highway a(n+39) = a(n)+13, the generation where it happens varies (3328, 25256, 66285, 177723, 255119, 354465, 415327).
FORMULA
a(n+39) = a(n)+13 for n > 66285.
CROSSREFS
Sequence in context: A268233 A309241 A065651 * A349049 A221356 A177329
KEYWORD
nonn
AUTHOR
Lars Blomberg, Aug 29 2019
STATUS
approved