A204371 Maximum period of cellular automaton rule 110 in a cyclic universe of width n.

1, 1, 1, 2, 1, 9, 14, 16, 7, 25, 110, 18, 351, 91, 295, 32, 578, 81, 285, 240, 630, 462, 1058, 552, 300, 351, 567, 2156, 1044, 1770, 2759, 2368, 1100, 969, 3920, 1584

Offset

1,4

Comments

a(n) >= A180001(n), and this sequence agrees with A180001 up to n=11.

Links

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

Eric Weisstein's World of Mathematics, Rule 110

Index entries for sequences related to cellular automata

Example

The 12 cell pattern
000100110111
001101111101
011111000111
110001001101
010011011111
110111110001
011100010011
110100110111
011101111100
110111000100
111101001101
000111011111
001101110001
011111010011
110001110111
010011011100
110111110100
111100011101
000100110111
Has period 18, which is the maximum possible, so a(12)=18

Mathematica

f[list_] := -Subtract @@ Flatten[Map[Position[#, #[[-1]]] &, NestWhileList[CellularAutomaton[110], list, Unequal, All], {0}]]; ma[n_] := Max[Table[f[IntegerDigits[i, 2, n]], {i, 0, 2^n - 1}]]; Table[ma[n], {n, 1, 10}]

Crossrefs

Cf. A180001, A161903, A006978, A332717, A332718.

Sequence in context: A072265 A192352 A180001 * A199887 A058876 A214884

Adjacent sequences: A204368 A204369 A204370 * A204372 A204373 A204374

Keyword

nonn,hard,more

Author

Ben Branman, Jan 14 2012

Extensions

a(19)-a(36) from Lars Blomberg, Dec 24 2015

Status

approved