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 A071030 Triangle read by rows giving successive states of cellular automaton generated by "Rule 54". 8
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row n has length 2n+1. 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 REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3. LINKS Michael De Vlieger, Table of n, a(n) for n = 0..10000 Michael De Vlieger, Visualization of rows 0 - 31 of Rule 54 S. Wolfram, Statistical mechanics of cellular automata, Rev. Mod. Phys., 55 (1983), 601--644. S. Wolfram, A New Kind of Science EXAMPLE From Michael De Vlieger, Oct 07 2015: (Start) First 12 rows, replacing "0" with "." for better visibility of ON cells:                         1                       1 1 1                     1 . . . 1                   1 1 1 . 1 1 1                 1 . . . 1 . . . 1               1 1 1 . 1 1 1 . 1 1 1             1 . . . 1 . . . 1 . . . 1           1 1 1 . 1 1 1 . 1 1 1 . 1 1 1         1 . . . 1 . . . 1 . . . 1 . . . 1       1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1     1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1   1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1 (End) MATHEMATICA 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 *) CROSSREFS Cf. A064455. See A118108 and A118109 for two other versions of this sequence. Sequence in context: A130630 A059318 A071029 * A104037 A014044 A014079 Adjacent sequences:  A071027 A071028 A071029 * A071031 A071032 A071033 KEYWORD nonn,tabf AUTHOR Hans Havermann, May 26 2002 EXTENSIONS Corrected by Hans Havermann, Jan 07 2012 STATUS approved

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