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%I #28 Jan 30 2016 14:39:07
%S 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 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 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 Triangle read by rows giving successive states of cellular automaton generated by "Rule 54".
%C Row n has length 2n+1.
%C 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 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
%H Michael De Vlieger, <a href="/A071030/b071030.txt">Table of n, a(n) for n = 0..10000</a>
%H Michael De Vlieger, <a href="/A071030/a071030.png">Visualization of rows 0 - 31 of Rule 54</a>
%H 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 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%e From _Michael De Vlieger_, Oct 07 2015: (Start)
%e First 12 rows, replacing "0" with "." for better visibility of ON cells:
%e 1
%e 1 1 1
%e 1 . . . 1
%e 1 1 1 . 1 1 1
%e 1 . . . 1 . . . 1
%e 1 1 1 . 1 1 1 . 1 1 1
%e 1 . . . 1 . . . 1 . . . 1
%e 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1
%e 1 . . . 1 . . . 1 . . . 1 . . . 1
%e 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1
%e 1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1
%e 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1
%e 1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1
%e (End)
%t 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 Cf. A064455. See A118108 and A118109 for two other versions of this sequence.
%K nonn,tabf
%O 0,1
%A _Hans Havermann_, May 26 2002
%E Corrected by _Hans Havermann_, Jan 07 2012
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