A326352 Total number of black cells after n iterations of Langton's ant with two ants on the grid placed side-by-side with one empty square between them and initially looking in the same direction.

0, 2, 4, 6, 8, 6, 6, 6, 6, 8, 6, 8, 10, 12, 14, 12, 12, 12, 12, 14, 12, 12, 12, 12, 14, 12, 14, 16, 18, 20, 18, 18, 16, 16, 18, 16, 18, 20, 22, 24, 22, 22, 22, 22, 24, 22, 22, 22, 22, 24, 22, 24, 26, 28, 30, 28, 28, 26, 26, 28, 28, 30, 30, 32, 34, 34, 36, 34

Offset: 0

Author

Felix Fröhlich, Jun 30 2019

Keywords

• nonn

Comments

The two ants meet seven times; in that case, the color of the current square is flipped only once. Eventually, both ants build a recurrent highway pattern. - Rémy Sigrist, Jul 28 2019

Examples

			See illustrations in Fröhlich, 2019.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..20000
• Felix Fröhlich, Illustration of iterations 0-50, 2019.
• Rémy Sigrist, Representation of the grid after 20000 iterations
• Rémy Sigrist, PARI program for A326352
• Wikipedia, Langton's ant

Crossrefs

Cf. A255938, A269757, A308590, A325953, A325954, A325955, A326167, A326353.

Programs

PARI

See Links section.

Formula

a(n + 104) = a(n) + 24 for any n >= 14373. - Rémy Sigrist, Jul 28 2019

Extensions

More terms from Rémy Sigrist, Jul 28 2019