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A325953 Langton's ant on a three-dimensional grid: number of black cells on the grid after n moves of the ant. 9
0, 1, 2, 3, 4, 3, 4, 5, 6, 6, 7, 8, 7, 8, 9, 10, 10, 9, 8, 8, 7, 6, 6, 6, 7, 8, 9, 9, 10, 11, 10, 11, 12, 11, 12, 13, 14, 14, 15, 16, 15, 16, 17, 18, 18, 17, 16, 16, 15, 14, 14, 14, 15, 16, 17, 17, 18, 19, 18, 19, 20, 19, 20, 21, 22, 22, 21, 20, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 to which the

  start of iteration | 90-degree turn |  cell is changed

  -------------------+----------------+-------------------

        white        |     right      |       black

        black        |     left       |       blue

        blue         |     up         |       yellow

        yellow       |     down       |       white

The first differences of this sequence are ultimately periodic with period 28 beginning at generation 93475, see A308563. - Charlie Neder, Jun 10 2019

LINKS

Table of n, a(n) for n=0..68.

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

Wikipedia, Langton's ant

Charlie Neder, Python program for running this automaton

EXAMPLE

See illustration in links.

CROSSREFS

Cf. A255938, A325954, A325955.

Sequence in context: A270652 A326693 A280242 * A245343 A255938 A081748

Adjacent sequences:  A325950 A325951 A325952 * A325954 A325955 A325956

KEYWORD

nonn

AUTHOR

Felix Fröhlich, May 28 2019

EXTENSIONS

a(51)-a(68) from Charlie Neder, Jun 06 2019

STATUS

approved

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Last modified June 4 02:54 EDT 2020. Contains 334812 sequences. (Running on oeis4.)