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

Author

Felix Fröhlich, Jul 10 2019

Keywords

• nonn

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.

Examples

			See illustrations in Fröhlich, 2019.
		

Links

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

Crossrefs

Cf. A326352.

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)