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

Author

Hans Havermann, May 26 2002

Keywords

• nonn
• tabf

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

Examples

			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)
		

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

Crossrefs

Cf. A064455. See A118108 and A118109 for two other versions of this sequence.

Programs

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 *)

Extensions

Corrected by Hans Havermann, Jan 07 2012