A243566 Triangle read by rows giving successive states of cellular automaton generated by "Rule 109" initiated with a single ON (black) cell.

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

Mathematica

rule=109; 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: A267848 A267179 A244527 * A266112 A331990 A301849

Adjacent sequences: A243563 A243564 A243565 * A243567 A243568 A243569

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 11 2016

Status

approved