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

0,2

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

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

Formula

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

Example

See illustrations in Fröhlich, 2019.

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A366637 A360700 A122640 * A299479 A185361 A245186

Adjacent sequences: A326349 A326350 A326351 * A326353 A326354 A326355

Keyword

nonn

Author

Felix Fröhlich, Jun 30 2019

Extensions

More terms from Rémy Sigrist, Jul 28 2019

Status

approved