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

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

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 * A355938 A268240 A104037

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