StatisticalMechanics / CONCEPT

ON cells of the Rule 41 cellular automaton

The elementary cellular automaton with Wolfram rule 41, started from a single ON cell at the origin and updated at every cell of the integers, has 1, 8k, 2 and 8k + 3 ON cells among the cells -n, ..., n of row n = 4k, 4k + 1, 4k + 2 and 4k + 3; the counts therefore satisfy Colin Barker's conjectured recurrence a(n) = a(n - 2) + a(n - 4) - a(n - 6) for n > 5 and generating function (1 + x^2 + 3x^3 - 2x^4 + 5x^5) / ((1 - x)^2 (1 + x)^2 (1 + x^2)) for OEIS A266614.