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A309075 Total number of black cells after n iterations of Langton's ant with two ants on the grid placed side-by-side on neighboring squares and initially looking in the same direction. 1
0, 2, 2, 4, 6, 6, 8, 8, 8, 6, 6, 4, 2, 2, 0, 2, 2, 4, 6, 6, 8, 8, 8, 6, 6, 4, 2, 2, 0, 2, 2, 4, 6, 6, 8, 8, 8, 6, 6, 4, 2, 2, 0, 2, 2, 4, 6, 6, 8, 8, 8, 6, 6, 4, 2, 2, 0, 2, 2, 4, 6, 6, 8, 8, 8, 6, 6, 4, 2, 2, 0, 2, 2, 4, 6, 6, 8, 8, 8, 6, 6, 4, 2, 2, 0, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Periodic with period 14.
The two ants are caught in a repeating cycle where they build and then erase a pattern of black cells, alternating between facing "northwards" and "southwards" on the completely white grid.
LINKS
FORMULA
Conjectures from Colin Barker, Jul 11 2019: (Start)
G.f.: 2*x*(1 + x)*(1 - x + x^2)*(1 + x^2)^2*(1 + x^4) / ((1 - x)*(1 - x + x^2 - x^3 + x^4 - x^5 + x^6)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).
a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6) + a(n-7) - a(n-8) + a(n-9) - a(n-10) + a(n-11) - a(n-12) + a(n-13) for n>12.
(End)
EXAMPLE
See illustrations in Fröhlich, 2019.
CROSSREFS
Cf. A326352.
Sequence in context: A098214 A178883 A109832 * A039731 A005341 A137268
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Jul 10 2019
STATUS
approved

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Last modified April 17 23:23 EDT 2024. Contains 371767 sequences. (Running on oeis4.)