A267800 Triangle read by rows giving successive states of cellular automaton generated by "Rule 213" initiated with a single ON (black) cell.

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

Offset

0

Comments

Row n has length 2n+1.

Links

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

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

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

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Example

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

Mathematica

rule=213; 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

Cf. A267801, A267802.

Cf. A267537 (central column), A267533 (row reversals).

Sequence in context: A307243 A120530 A078616 * A373993 A322980 A267053

Adjacent sequences: A267797 A267798 A267799 * A267801 A267802 A267803

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 20 2016

Status

approved