A267136 Triangle read by rows giving successive states of cellular automaton generated by "Rule 103" initiated with a single ON (black) cell.

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

Mathematica

rule=103; 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: A074201 A143466 A195053 * A117908 A115360 A088911

Adjacent sequences: A267133 A267134 A267135 * A267137 A267138 A267139

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 10 2016

Status

approved