cp's OEIS Frontend

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

%I A204371 #20 Feb 16 2025 08:33:16
%S A204371 1,1,1,2,1,9,14,16,7,25,110,18,351,91,295,32,578,81,285,240,630,462,
%T A204371 1058,552,300,351,567,2156,1044,1770,2759,2368,1100,969,3920,1584
%N A204371 Maximum period of cellular automaton rule 110 in a cyclic universe of width n.
%C A204371 a(n) >= A180001(n), and this sequence agrees with A180001 up to n=11.
%H A204371 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule110.html">Rule 110</a>
%H A204371 <a href="http://oeis.org/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%e A204371 The 12 cell pattern
%e A204371 000100110111
%e A204371 001101111101
%e A204371 011111000111
%e A204371 110001001101
%e A204371 010011011111
%e A204371 110111110001
%e A204371 011100010011
%e A204371 110100110111
%e A204371 011101111100
%e A204371 110111000100
%e A204371 111101001101
%e A204371 000111011111
%e A204371 001101110001
%e A204371 011111010011
%e A204371 110001110111
%e A204371 010011011100
%e A204371 110111110100
%e A204371 111100011101
%e A204371 000100110111
%e A204371 Has period 18, which is the maximum possible, so a(12)=18
%t A204371 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}]
%Y A204371 Cf. A180001, A161903, A006978, A332717, A332718.
%K A204371 nonn,hard,more
%O A204371 1,4
%A A204371 _Ben Branman_, Jan 14 2012
%E A204371 a(19)-a(36) from _Lars Blomberg_, Dec 24 2015