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.

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

Author

Felix Fröhlich, Sep 07 2019

Keywords

• nonn

Comments

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.

Examples

			See illustrations in Fröhlich, 2019.
		

Links

• 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

Crossrefs

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

Formula

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

Extensions

More terms from Jinyuan Wang, Jul 15 2025