A267253 Triangle read by rows giving successive states of cellular automaton generated by "Rule 111" initiated with a single ON (black) cell.

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

Mathematica

rule=111; 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. A267254, A267255, A267358 (rows reversed).

Sequence in context: A179763 A257341 A284512 * A261178 A204439 A204443

Adjacent sequences: A267250 A267251 A267252 * A267254 A267255 A267256

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 12 2016

Status

approved