

A309166


Langton's ant on a truncated hexagonal tiling: number of black cells after n moves of the ant when starting on a dodecagon and looking towards an edge where the dodecagon meets a triangle.


5



0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 10, 11, 12, 13, 12, 11, 12, 13, 14, 15, 16, 15, 14, 15, 16, 17, 18, 19, 20, 19, 18, 17, 16, 17, 18, 19, 20, 21, 22, 23, 22, 23, 24, 25, 26, 27, 26, 27, 28, 29, 30, 31, 30, 29, 30, 31, 32, 33, 34, 33, 32, 33, 32
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OFFSET

0,3


COMMENTS

On a white dodecagon, turn 30 degrees right, flip the color of the tile, then move forward one unit.
On a black dodecagon, turn 30 degrees left, 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 triangle, turn 60 degrees left, flip the color of the tile, then move forward one unit.


LINKS

Sean A. Irvine, Table of n, a(n) for n = 0..10000
Lars Blomberg, The state for n=2200, when 342 cells are set
Lars Blomberg, Animation illustrating n=12200
Felix Fröhlich, Illustration of iterations 050 of the ant, 2019.
Sean A. Irvine, Java program (github)
Wikipedia, Langton's ant
Wikipedia, Truncated hexagonal tiling


FORMULA

a(n+15) = a(n) + 9 for n > 2034.  Lars Blomberg, Aug 13 2019


EXAMPLE

See illustrations in Fröhlich, 2019.


CROSSREFS

Cf. A255938, A269757, A308590, A308937, A308973, A326167, A326352, A309064.
Sequence in context: A017894 A291571 A232897 * A028903 A081599 A289642
Adjacent sequences: A309163 A309164 A309165 * A309167 A309168 A309169


KEYWORD

nonn


AUTHOR

Felix Fröhlich, Jul 15 2019


EXTENSIONS

More terms from Sean A. Irvine, Jul 22 2019


STATUS

approved



