A325954 Langton's ant on a three-dimensional grid: number of blue cells on the grid after n moves of the ant.

0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 2, 2, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 5, 5, 5, 5, 4, 5, 6, 6, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 8, 9, 10, 9, 9, 10, 10, 10, 10, 9, 8, 8, 8, 7, 8, 8, 8, 8, 7, 8, 9

Offset

0,19

Comments

The ant starts on a completely white grid.

Order of operations: turn 90 degrees, change cell color, move forward one unit.

The rules governing the movement of the ant and the change of cell colors are shown in the following table:

Cell color at | Direction of | Color the cell is

start of iteration | 90-degree turn | changed to

--------------------------------------------------------

white | right | black

black | left | blue

blue | up | yellow

yellow | down | white

Links

Jinyuan Wang, Table of n, a(n) for n = 0..10000

Felix Fröhlich, Illustration of iterations 0-50 of the ant

Wikipedia, Langton's ant

Formula

a(n) = a(n-28) + 2 for n >= 93504. - Jinyuan Wang, Jul 13 2025

Example

See illustration in links.

Crossrefs

Cf. A255938, A308563, A325953, A325955.

Sequence in context: A185068 A078664 A328388 * A390506 A243503 A069581

Adjacent sequences: A325951 A325952 A325953 * A325955 A325956 A325957

Keyword

nonn

Author

Felix Fröhlich, May 28 2019

Extensions

a(51)-a(80) from Charlie Neder, Jun 06 2019

Status

approved