A308937 Langton's ant on a chair tiling: number of black cells after n moves of the ant.

0, 1, 2, 3, 4, 3, 4, 5, 6, 5, 4, 5, 6, 7, 8, 7, 8, 9, 10, 9, 10, 9, 10, 11, 12, 11, 10, 9, 10, 9, 10, 11, 12, 13, 12, 13, 14, 15, 14, 15, 14, 15, 16, 17, 16, 15, 14, 15, 14, 15, 16, 17, 18, 17, 18, 19, 20, 21, 20, 19, 20, 19, 20, 19, 18, 17, 18, 19, 20, 21, 20

Offset: 0

Author

Felix Fröhlich, Jul 01 2019

Keywords

• nonn
• easy

Comments

The ant begins on the inner corner of a subtile.

On a white tile, turn 90 degrees right, flip the color of the tile, then move forward until reaching a new tile, moving as far as possible within the tile.

On a black tile, turn 90 degrees left, then continue as above.

The chair tiling used for this automaton is, like all aperiodic hierarchical tilings, not unique (see for example Goodman-Strauss, p. 490). See "Remarks, 2019" in links for clarification which tiling the ant lives on.

Examples

			See illustrations in Fröhlich, 2019.
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 0..1000
• Felix Fröhlich, Illustration of iterations 0-50 of the ant, 2019.
• Felix Fröhlich, Remarks specifying the tiling used for generating the sequence, 2019.
• Chaim Goodman-Strauss, Aperiodic Hierarchical Tilings, in: J. F. Sadoc and N. Rivier, Foams and Emulsions, NATO Science Series, Series E, Vol. 354, Springer, pp 481-496, DOI:10.1007/978-94-015-9157-7_28.
• Tilings Encyclopedia, Chair
• Wikipedia, Langton's ant
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A255938, A269757, A308590, A325953, A325954, A325955.

Formula

a(n) = a(n-42) for n >= 178. - Jinyuan Wang, Jul 13 2025

Extensions

More terms from Jinyuan Wang, Jul 13 2025