%I #12 Jul 25 2019 08:31:18
%S 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,
%T 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,
%U 2,2,0,2,2,4,6,6,8,8,8,6,6,4,2,2,0,2,2
%N 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.
%C Periodic with period 14.
%C 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.
%H Felix Fröhlich, <a href="/A309075/a309075.pdf">Illustration of iterations 014 of the ants</a>, 2019.
%F Conjectures from _Colin Barker_, Jul 11 2019: (Start)
%F 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)).
%F 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.
%F (End)
%e See illustrations in Fröhlich, 2019.
%Y Cf. A326352.
%K nonn
%O 0,2
%A _Felix Fröhlich_, Jul 10 2019
