A267676 Triangle read by rows giving successive states of cellular automaton generated by "Rule 197" initiated with a single ON (black) cell.

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

Mathematica

rule=197; 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: A266840 A104606 A189169 * A014389 A014349 A014269

Adjacent sequences: A267673 A267674 A267675 * A267677 A267678 A267679

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 19 2016

Status

approved