A267463 Triangle read by rows giving successive states of cellular automaton generated by "Rule 137" initiated with a single ON (black) cell.

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

Mathematica

rule=137; 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: A352679 A239199 A265718 * A264442 A266243 A266608

Adjacent sequences: A267460 A267461 A267462 * A267464 A267465 A267466

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 15 2016

Status

approved