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A071030 Triangle read by rows giving successive states of cellular automaton generated by "Rule 54".

%I A071030 #28 Jan 30 2016 14:39:07
%S A071030 1,1,1,1,1,0,0,0,1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,1,1,1,0,1,1,1,0,1,
%T A071030 1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,1,0,0,0,
%U A071030 1,0,0,0,1,0,0,0,1,0,0,0,1,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1
%N A071030 Triangle read by rows giving successive states of cellular automaton generated by "Rule 54".
%C A071030 Row n has length 2n+1.
%C A071030 Even rows r sum to r/2 + 1, odd rows r sum to 3r to produce the sequence {1, 3, 2, 6, 3, 9, 4, 12, ...} = A064455(n + 1). - _Michael De Vlieger_, Oct 07 2015
%D A071030 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
%H A071030 Michael De Vlieger, <a href="/A071030/b071030.txt">Table of n, a(n) for n = 0..10000</a>
%H A071030 Michael De Vlieger, <a href="/A071030/a071030.png">Visualization of rows 0 - 31 of Rule 54</a>
%H A071030 S. Wolfram, <a href="http://dx.doi.org/10.1103/RevModPhys.55.601">Statistical mechanics of cellular automata</a>, Rev. Mod. Phys., 55 (1983), 601--644.
%H A071030 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A071030 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A071030 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%e A071030 From _Michael De Vlieger_, Oct 07 2015: (Start)
%e A071030 First 12 rows, replacing "0" with "." for better visibility of ON cells:
%e A071030                         1
%e A071030                       1 1 1
%e A071030                     1 . . . 1
%e A071030                   1 1 1 . 1 1 1
%e A071030                 1 . . . 1 . . . 1
%e A071030               1 1 1 . 1 1 1 . 1 1 1
%e A071030             1 . . . 1 . . . 1 . . . 1
%e A071030           1 1 1 . 1 1 1 . 1 1 1 . 1 1 1
%e A071030         1 . . . 1 . . . 1 . . . 1 . . . 1
%e A071030       1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1
%e A071030     1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1
%e A071030   1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1
%e A071030 1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1
%e A071030 (End)
%t A071030 clip[lst_] := Block[{p = Flatten@ Position[lst, 1]}, Take[lst, {Min@ p, Max@ p}]]; clip /@ CellularAutomaton[54, {{1}, 0}, 8] // Flatten (* _Michael De Vlieger_, Oct 07 2015 *)
%Y A071030 Cf. A064455. See A118108 and A118109 for two other versions of this sequence.
%K A071030 nonn,tabf
%O A071030 0,1
%A A071030 _Hans Havermann_, May 26 2002
%E A071030 Corrected by _Hans Havermann_, Jan 07 2012