A323382 - OEIS

%I #15 Feb 25 2019 20:58:19

%S 2,3,2,5,8,3,20,14,26,3,36,5,106,3,14,29,48,3,80,67,156,3,74,14,594,3,

%T 26,93,440,3,380,115,1062,3,1826,82,1864,3,1488,2603,328,3,1714,10229,

%U 2330,3,1372,23,15202,3,43186,7524,49534,3,69612,9508,5112,3,1260,54687

%N a(n) is the period of the oscillating pattern formed by a diagonal line of 2*n cells in the Life-like cellular automaton B2e3ijkn4cz5/S236.

%C An explanation of the Hensel notation used to define the cellular automaton rule can be found on the LifeWiki (see links).

%C Lines of odd lengths are excluded because they break up into patterns not consisting of diagonal lines.

%C These diagonal line oscillators are effectively emulating a four-state one-dimensional cellular automaton.

%C From _Charlie Neder_, Feb 12 2019: (Start)

%C Specifically, such an oscillator with 2*n cells is isomorphic to a row of 2*n state-1 cells that evolve according to the following rules:

%C 1) A state-1 cell becomes state-3 if it has a state-1 neighbor, and state-2 otherwise,

%C 2) A state-2 cell becomes state-1 unconditionally,

%C 3) A state-3 cell becomes state-1 if both its neighbors are state-3, and state-2 otherwise. (End)

%H LifeWiki, <a href="http://www.conwaylife.com/wiki/Isotropic_non-totalistic_Life-like_cellular_automaton">Isotropic non-totalistic Life-like cellular automaton</a>

%F If n == 2 (mod 4), a(n) = 3.

%e a(4) = 5 because a diagonal line of 8 cells oscillates with period 5 in this cellular automaton.

%K nonn

%O 1,1

%A _WG Zeist_, Jan 12 2019