This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309075 #12 Jul 25 2019 08:31:18 %S A309075 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 A309075 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 A309075 2,2,0,2,2,4,6,6,8,8,8,6,6,4,2,2,0,2,2 %N 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. %C A309075 Periodic with period 14. %C A309075 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 A309075 Felix Fröhlich, <a href="/A309075/a309075.pdf">Illustration of iterations 0-14 of the ants</a>, 2019. %F A309075 Conjectures from _Colin Barker_, Jul 11 2019: (Start) %F A309075 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 A309075 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. %F A309075 (End) %e A309075 See illustrations in Fröhlich, 2019. %Y A309075 Cf. A326352. %K A309075 nonn %O A309075 0,2 %A A309075 _Felix Fröhlich_, Jul 10 2019