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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

Index to Elementary Cellular Automata

Index entries for sequences related to cellular automata

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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Last modified March 23 19:17 EDT 2017. Contains 283957 sequences.