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A308973
Langton's ant on a truncated square tiling: number of black cells after n moves of the ant when starting on an octagon and looking towards an edge where the tile meets another octagon.
8
0, 1, 2, 3, 4, 5, 6, 5, 6, 7, 8, 9, 8, 7, 8, 9, 10, 11, 10, 11, 10, 9, 10, 11, 12, 13, 14, 15, 14, 15, 16, 17, 18, 17, 16, 17, 18, 17, 16, 17, 18, 19, 20, 21, 22, 21, 22, 23, 24, 23, 22, 23, 24, 25, 26, 27, 28, 27, 28, 29, 30, 29, 28, 29, 30, 31, 32, 33, 34
OFFSET
0,3
COMMENTS
First differs from A269757 at n = 19.
On a white square, turn 90 degrees right, flip the color of the tile, then move forward one unit.
On a white octagon, turn 45 degrees right, flip the color of the tile, then move forward one unit.
On a black square, turn 90 degrees left, flip the color of the tile, then move forward one unit.
On a black octagon, turn 45 degrees left, flip the color of the tile, then move forward one unit.
As in the original variant, order emerges after a transition phase and the ant starts building a recurrent "highway" pattern of 12 steps that repeats indefinitely. - Rémy Sigrist, Jul 21 2019
FORMULA
a(n + 12) = a(n) + 6 for any n >= 34. - Rémy Sigrist, Jul 21 2019
EXAMPLE
See illustrations in Fröhlich, 2019.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Jul 04 2019
EXTENSIONS
More terms from Rémy Sigrist, Jul 21 2019
STATUS
approved