A266619 Triangle read by rows giving successive states of cellular automaton generated by "Rule 45" initiated with a single ON (black) cell.

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

Offset

0

Comments

Row n has length 2n+1.

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

G. C. Greubel, Table of n, a(n) for n = 0..3599

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
                0 1 1 1 1
              1 0 1 0 0 0 0
            0 0 1 1 0 1 1 0 1
          1 1 0 1 0 1 1 0 1 1 0
        0 0 0 1 1 1 1 0 1 1 0 1 1
      1 1 1 0 1 0 0 0 1 1 0 1 1 0 0
    0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1
  1 1 1 1 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0

Mathematica

rule=45; 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: A129407 A267594 A273512 * A267587 A380418 A014165

Adjacent sequences: A266616 A266617 A266618 * A266620 A266621 A266622

Keyword

nonn,tabf,easy,changed

Author

Robert Price, Jan 01 2016

Status

approved