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%I #8 Mar 30 2012 19:00:48
%S 1,2,2,2,1,2,14,4,22,2,121,5,143,14,55,26,17,22,171,180,189,198,207
%N Maximum period of the totalistic 2-color radius 2 cellular automaton in a cyclic universe of width n.
%C A cell's neighborhood consists of itself, the two cells to its left, and the two cells to its right. A cell becomes live if it had either two or four live neighbors (including itself) in the previous generation.
%D Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, 2002, p. 255-260, p. 281-285
%e For n=7, the initial state 0, 0, 1, 1, 0, 1, 0 has evolution:
%e 0011010
%e 1110010
%e 1000110
%e 1011100
%e 1010001
%e 0010111
%e 0110100
%e 1100101
%e 0001101
%e 0111001
%e 0100011
%e 0101110
%e 1101000
%e 1001011
%e 0011010
%e Which has period 14, the highest possible. Thus a(7)=14.
%t f[list_] := -Subtract @@ Flatten[Map[Position[#, #[[-1]]] &, NestWhileList[CellularAutomaton[{20, {2, 1}, 2}], list, Unequal, All], {0}]]; a[n_] := Max[Table[f[IntegerDigits[i, 2, n]], {i, 0, 2^n - 1}]]; Table[a[n], {n, 1, 12}]
%Y Cf. A204371, A204714.
%K nonn,hard
%O 1,2
%A _Ben Branman_, Jan 29 2012
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