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A204714
Maximum period of cellular automaton rule 54 in a cyclic universe of width n.
1
1, 1, 1, 4, 1, 4, 4, 8, 27, 30, 99, 12, 169, 112, 330, 40, 289, 306, 494, 86, 399, 484, 690, 312, 1800, 624, 918, 224, 783, 780, 1240, 608, 1056, 952, 1540, 684
OFFSET
1,4
EXAMPLE
For n=8, the initial condition 00011101 yields the evolution
00011101
10100011
01110100
10001110
11010001
00111010
01000111
11101000
00011101
Which is period 8, the maximum possible, so a(8)=8.
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ben Branman, Jan 18 2012
EXTENSIONS
a(15)-a(36) from Lars Blomberg, Dec 24 2015
STATUS
approved