A267636 Triangle read by rows giving successive states of cellular automaton generated by "Rule 193" initiated with a single ON (black) cell.

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

Mathematica

rule=193; 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: A353488 A232991 A168553 * A267841 A309850 A262448

Adjacent sequences: A267633 A267634 A267635 * A267637 A267638 A267639

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 18 2016

Status

approved