A267037 Triangle read by rows giving successive states of cellular automaton generated by "Rule 89" initiated with a single ON (black) cell.

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

Mathematica

rule=89; 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: A072792 A254113 A365495 * A200246 A267292 A267178

Adjacent sequences: A267034 A267035 A267036 * A267038 A267039 A267040

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 09 2016

Status

approved