A267423 Triangle read by rows giving successive states of cellular automaton generated by "Rule 133" initiated with a single ON (black) cell.

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

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

Mathematica

rule=133; 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: A005369 A278169 A262693 * A108340 A341040 A257585

Adjacent sequences: A267420 A267421 A267422 * A267424 A267425 A267426

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 14 2016

Status

approved