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

Author

Ben Branman, Jan 14 2012

Keywords

• nonn
• hard
• more

Comments

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

Examples

			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
		

Links

• Eric Weisstein's World of Mathematics, Rule 110
• Index entries for sequences related to cellular automata

Crossrefs

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

Programs

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}]

Extensions

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