A267358 Triangle read by rows giving successive states of cellular automaton generated by "Rule 125" initiated with a single ON (black) cell.

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

Mathematica

rule=125; 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: A188038 A275694 A267922 * A368281 A153860 A254377

Adjacent sequences: A267355 A267356 A267357 * A267359 A267360 A267361

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 13 2016

Status

approved