

A309075


Total number of black cells after n iterations of Langton's ant with two ants on the grid placed sidebyside 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
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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

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(n1)  a(n2) + a(n3)  a(n4) + a(n5)  a(n6) + a(n7)  a(n8) + a(n9)  a(n10) + a(n11)  a(n12) + a(n13) for n>12.
(End)


EXAMPLE

See illustrations in Fröhlich, 2019.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



