A309279 -id:A309279 - cp's OEIS frontend

A309293 Langton's ant on a snub trihexagonal tiling: number of black cells after n moves of the ant when starting on a hexagon.

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

Offset: 0

Felix Fröhlich, Jul 21 2019

nonn

On a white tile, turn 60 degrees right, flip the color of the tile, then move forward one unit.
On a black tile, turn 60 degrees left, flip the color of the tile, then move forward one unit.
The sequence has a cycle of length of 28292, that is, a(28292)=0 with the ant in the starting hexagon pointing in the start direction, so another cycle will follow. The maximum term in the cycle is a(8148)=174. - Lars Blomberg, Aug 01 2019

			See illustrations in Fröhlich, 2019.

Lars Blomberg, Table of n, a(n) for n = 0..28292
Lars Blomberg, The state for n=8148, when 174 cells are set
Lars Blomberg, Video illustrating a full cycle
Felix Fröhlich, Illustration of iterations 0-50 of the ant, 2019.
Wikipedia, Langton's ant
Wikipedia, Snub trihexagonal tiling

Cf. A255938, A269757, A308590, A308937, A308973, A326167, A326352, A309064, A309166, A309241, A309279.

More terms from Lars Blomberg, Aug 01 2019

A325631 Langton's ant on an elongated triangular tiling: number of black cells after n moves of the ant when starting on a square and initially looking towards one of the edges where that square meets one of the neighboring triangles.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 4, 5, 6, 7, 8, 9, 8, 9, 10, 11, 12, 13, 12, 13, 14, 15, 14, 13, 14, 15, 16, 15, 16, 17, 16, 15, 16, 17, 18, 17, 16, 15, 16, 17, 18, 19, 20, 19, 18, 19, 20, 19, 20, 21, 22, 23, 24, 23, 22, 23, 22, 23, 22, 21, 20, 19, 18, 19, 18, 17, 18, 19, 20

Offset: 0

Felix Fröhlich, Sep 07 2019

nonn

First differs from A276073 at n = 22.
On a white square, turn 90 degrees right, 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 square, turn 90 degrees left, 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.

			See illustrations in Fröhlich, 2019.

Jinyuan Wang, Table of n, a(n) for n = 0..2000
Felix Fröhlich, Illustration of iterations 0-50 of the ant, 2019.
Wikipedia, Elongated triangular tiling
Wikipedia, Langton's ant

Cf. A255938, A269757, A308590, A308937, A308973, A326167, A326352, A309064, A309166, A309241, A309279, A309293.

a(n) = a(n-51) + 11 for n >= 1159. - Jinyuan Wang, Jul 15 2025

More terms from Jinyuan Wang, Jul 15 2025

cp's OEIS Frontend

A309293 Langton's ant on a snub trihexagonal tiling: number of black cells after n moves of the ant when starting on a hexagon.

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