A309166 Langton's ant on a truncated hexagonal tiling: 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 triangle.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 10, 11, 12, 13, 12, 11, 12, 13, 14, 15, 16, 15, 14, 15, 16, 17, 18, 19, 20, 19, 18, 17, 16, 17, 18, 19, 20, 21, 22, 23, 22, 23, 24, 25, 26, 27, 26, 27, 28, 29, 30, 31, 30, 29, 30, 31, 32, 33, 34, 33, 32, 33, 32

Offset: 0

Author

Felix Fröhlich, Jul 15 2019

Keywords

• nonn

Comments

On a white dodecagon, turn 30 degrees right, flip the color of the tile, then move forward one unit.

On a black dodecagon, turn 30 degrees left, flip the color of the tile, then move forward one unit.

On a white triangle, turn 60 degrees right, flip the color of the tile, then move forward one unit.

On a black triangle, turn 60 degrees left, flip the color of the tile, then move forward one unit.

Examples

			See illustrations in Fröhlich, 2019.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 0..10000
• Lars Blomberg, The state for n=2200, when 342 cells are set
• Lars Blomberg, Animation illustrating n=1-2200
• Felix Fröhlich, Illustration of iterations 0-50 of the ant, 2019.
• Sean A. Irvine, Java program (github)
• Wikipedia, Langton's ant
• Wikipedia, Truncated hexagonal tiling

Crossrefs

Cf. A255938, A269757, A308590, A308937, A308973, A326167, A326352, A309064.

Formula

a(n+15) = a(n) + 9 for n > 2034. - Lars Blomberg, Aug 13 2019

Extensions

More terms from Sean A. Irvine, Jul 22 2019