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.

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

Lars Blomberg, Table of n, a(n) for n = 0..276

Formula

a(n+276) = a(n).

Crossrefs

Sequence in context: A360535 A255938 A081748 * A030323 A285872 A227181

Adjacent sequences: A322287 A322288 A322289 * A322291 A322292 A322293

Keyword

nonn

Author

Lars Blomberg, Aug 28 2019

Status

approved