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.

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

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