A266178 Triangle read by rows giving successive states of cellular automaton generated by "Rule 6" initiated with a single ON (black) cell.

1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0

Offset

0

Comments

Row n has length 2n+1.

The sequence is also generated by Rules 38, 134 and 166.

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

Robert Price, Table of n, a(n) for n = 0..9999

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Example

The first ten rows:
                  1
                1 1 0
              1 0 0 0 0
            1 1 0 0 0 0 0
          1 0 0 0 0 0 0 0 0
        1 1 0 0 0 0 0 0 0 0 0
      1 0 0 0 0 0 0 0 0 0 0 0 0
    1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Mathematica

rule=6; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Flatten[catri] (* Triangle Representation of CA *)

Crossrefs

Sequence in context: A071002 A113431 A116915 * A339653 A255738 A296209

Adjacent sequences: A266175 A266176 A266177 * A266179 A266180 A266181

Keyword

nonn,tabf,easy

Author

Robert Price, Dec 22 2015

Status

approved