A267810 Triangle read by rows giving successive states of cellular automaton generated by "Rule 217" initiated with a single ON (black) cell.

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

Mathematica

rule=217; 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: A267178 A285277 A116937 * A267927 A030300 A168394

Adjacent sequences: A267807 A267808 A267809 * A267811 A267812 A267813

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 20 2016

Status

approved