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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

Table of n, a(n) for n=0..86.

Felix Fröhlich, Illustration of iterations 0-14 of the ants, 2019.

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

Adjacent sequences:  A309072 A309073 A309074 * A309076 A309077 A309078

KEYWORD

nonn

AUTHOR

Felix Fröhlich, Jul 10 2019

STATUS

approved

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Last modified February 21 18:05 EST 2020. Contains 332107 sequences. (Running on oeis4.)