login
A322290
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.
1
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, 10, 11, 12, 13, 12, 13, 14, 15, 16, 17, 18, 17, 18, 19, 20, 21, 20, 19, 20, 19, 18, 17, 18, 19, 18, 17, 16, 15, 14, 15, 16, 15, 14, 15, 16, 17, 18, 17, 16, 15, 14
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).
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.
Many other starting positions are possible which give different terms. While they all eventually repeat the cycle, lengths vary (68, 96, 276, 1320, 2092).
LINKS
FORMULA
a(n+276) = a(n).
CROSSREFS
Sequence in context: A360535 A255938 A081748 * A030323 A285872 A227181
KEYWORD
nonn
AUTHOR
Lars Blomberg, Aug 28 2019
STATUS
approved