A267813 Triangle read by rows giving successive states of cellular automaton generated by "Rule 219" initiated with a single ON (black) cell.

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

Offset

0

Comments

Row n has length 2n+1.

References

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

Links

Robert Price, Table of n, a(n) for n = 0..10000

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 0 1
              1 1 0 1 1
            1 1 1 0 1 1 1
          1 1 1 1 0 1 1 1 1
        1 1 1 1 1 0 1 1 1 1 1
      1 1 1 1 1 1 0 1 1 1 1 1 1
    1 1 1 1 1 1 1 0 1 1 1 1 1 1 1
  1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1

Mathematica

rule=219; 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: A284386 A286922 A285668 * A323000 A005713 A188031

Adjacent sequences: A267810 A267811 A267812 * A267814 A267815 A267816

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 20 2016

Status

approved