A204714 Maximum period of cellular automaton rule 54 in a cyclic universe of width n.

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

Links

Table of n, a(n) for n=1..36.

Index entries for sequences related to cellular automata

Eric Weisstein's World of Mathematics, Rule 54

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

Cf. A071030, A118108

Sequence in context: A035646 A144034 A366887 * A341100 A350639 A347264

Adjacent sequences: A204711 A204712 A204713 * A204715 A204716 A204717

Keyword

nonn

Author

Ben Branman, Jan 18 2012

Extensions

a(15)-a(36) from Lars Blomberg, Dec 24 2015

Status

approved