A204714 - OEIS

%I #11 Dec 24 2015 10:33:06

%S 1,1,1,4,1,4,4,8,27,30,99,12,169,112,330,40,289,306,494,86,399,484,

%T 690,312,1800,624,918,224,783,780,1240,608,1056,952,1540,684

%N Maximum period of cellular automaton rule 54 in a cyclic universe of width n.

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rule54.html">Rule 54</a>

%e For n=8, the initial condition 00011101 yields the evolution

%e 00011101

%e 10100011

%e 01110100

%e 10001110

%e 11010001

%e 00111010

%e 01000111

%e 11101000

%e 00011101

%e Which is period 8, the maximum possible, so a(8)=8.

%t f[list_] := -Subtract @@ Flatten[Map[Position[#, #[[-1]]] &, NestWhileList[CellularAutomaton[54], list, Unequal, All], {0}]]; a[n_] := Max[Table[f[IntegerDigits[i, 2, n]], {i, 0, 2^n - 1}]]; Table[a[n], {n, 1, 10}]

%Y Cf. A071030, A118108

%K nonn

%O 1,4

%A _Ben Branman_, Jan 18 2012

%E a(15)-a(36) from _Lars Blomberg_, Dec 24 2015